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All Textbook Solutions for Elementary Algebra

In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 96. 24=p20 In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 97. y=6 In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 98. u=15 In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 99. v=72 In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 100. x=39 In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 101. 23y=48 In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 102. 35r=75 In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 103. 58w=40 In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 104. 24=34x In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 105. 25=110a In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 106. 13q=56 In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 107. 710x=143 In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 108. 38y=14 In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 109. 712=34p In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 110. 1118=56q In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 111. 518=109u In the following exercises, solve each equation using the Division and Multiplication Properties of Equality and check the solution. 112. 720=74v In the following exercises, solve each equation requiring simplification. 113. 10016=4p10pp In the following exercises, solve each equation requiring simplification. 114. 187=5t9t6t In the following exercises, solve each equation requiring simplification. 115. 78n34n=9+2 In the following exercises, solve each equation requiring simplification. 116. 512q+12q=253 In the following exercises, solve each equation requiring simplification. 117. 0.25d+0.10d=60.75 In the following exercises, solve each equation requiring simplification. 118. 0.05p0.01p=2+0.24 In the following exercises, solve each equation requiring simplification. 119. 10(q4)57=93 In the following exercises, solve each equation requiring simplification. 120. 12(d5)29=43 In the following exercises, solve each equation requiring simplification. 121. 10(x+4)19=85 In the following exercises, solve each equation requiring simplification. 122. 15(z+9)11=75 In the following exercises, solve each equation. 123. 910x=90 In the following exercises, solve each equation. 124. 512y=60 In the following exercises, solve each equation. 125. y+46=55 In the following exercises, solve each equation. 126. x+33=41 In the following exercises, solve each equation. 127. w2=99 In the following exercises, solve each equation. 128. s3=60 In the following exercises, solve each equation. 129. 27=6a In the following exercises, solve each equation. 130. a=7 In the following exercises, solve each equation. 131. x=2 In the following exercises, solve each equation. 132. z16=59 In the following exercises, solve each equation. 133. m41=14 In the following exercises, solve each equation. 134. 0.04r=52.60 In the following exercises, solve each equation. 135. 63.90=0.03p In the following exercises, solve each equation. 136. 15x=120 In the following exercises, solve each equation. 137. 84=12z In the following exercises, solve each equation. 138. 19.36=x0.2x In the following exercises, solve each equation. 139. c0.3c=35.70 In the following exercises, solve each equation. 140. y=9 In the following exercises, solve each equation. 141. x=8 In the following exercises, translate to an equation and then solve. 142. 187 is the product of 17 and m.In the following exercises, translate to an equation and then solve. 143. 133 is the product of 19 and n.In the following exercises, translate to an equation and then solve. 144. 184 is the product of 23 and p.In the following exercises, translate to an equation and then solve. 145. 152 is the product of 8 and q.In the following exercises, translate to an equation and then solve. 146. u divided by 7 is equal to 49 .In the following exercises, translate to an equation and then solve. 147. r divided by 12 is equal to 48 .In the following exercises, translate to an equation and then solve. 148. h divided by 13 is equal to 65 .In the following exercises, translate to an equation and then solve. 149. j divided by 20 is equal to 80 .In the following exercises, translate to an equation and then solve. 150. The quotient c and 19 is 38.In the following exercises, translate to an equation and then solve. 151. The quotient of b and 6 is 18.In the following exercises, translate to an equation and then solve. 152. The quotient of h and 26 is 52 .In the following exercises, translate to an equation and then solve. 153. The quotient k and 22 is -66.In the following exercises, translate to an equation and then solve. 154. Five-sixths of y is 15.In the following exercises, translate to an equation and then solve. 155. Three-tenths of x is 15.In the following exercises, translate to an equation and then solve. 156. Four-thirds of w is 36.In the following exercises, translate to an equation and then solve. 157. Five-halves of v is 50.In the following exercises, translate to an equation and then solve. 158. The sum of nine-tenths and g is two-thirds.In the following exercises, translate to an equation and then solve. 159. The sum of two-fifths and f is one-half.In the following exercises, translate to an equation and then solve. 160. The difference of p and one-sixth is two-thirds.In the following exercises, translate to an equation and then solve. 161. The difference of q and one-eighth is three-fourths.In the following exercises, translate into an equation and solve. 162. Kindergarten Connie’s kindergarten class has 24 children. She wants them to get into 4 equal groups. How many children will she put in each group?In the following exercises, translate into an equation and solve. 163. Balloons Ramona bought 18 balloons for a party. She wants to make 3 equal bunches. How many balloons did she use in each bunch?In the following exercises, translate into an equation and solve. 164. Tickets Mollie paid $36.25 for 5 movie tickets. What was the price of each ticket?In the following exercises, translate into an equation and solve. 165. Shopping Serena paid $12.96 for a pack of 12 pairs of sport socks. What was the price of pair of sport socks?In the following exercises, translate into an equation and solve. 166. Sewing Nancy used 14 yards of fabric to make flags for one-third of the drill team. How much fabric, would Nancy need to make flags for the whole team?In the following exercises, translate into an equation and solve. 167. MPG John’s SUV gets 18 miles per gallon (mpg). This is half as many mpg as his wife’s hybrid car. How many miles per gallon does the hybrid car get?In the following exercises, translate into an equation and solve. 168. Height Aiden is 27 inches tall. He is 38 as tall as his father. How tall is his father?In the following exercises, translate into an equation and solve. 169. Real estate Bea earned $11,700 commission for selling a house, calculated as 6100 of the selling price. What was the selling price of the house?Commission Every week Perry gets paid $150 plus 12% of his total sales amount. Solve the equation 840=150+0.12(a1250) for a, to find the total amount Perry must sell in order to be paid $840 one week.Stamps Travis bought $9.45 worth of 49-cent stamps and 21-cent stamps. The number of 21-cent stamps was 5 less than the number of 49-cent stamps. Solve the equation 0.49s+0.21(s5)=9.45 for s, to find the number of 49-cent stamps Travis bought.Frida started to solve the equation 3x=36 by adding 3 to both sides. Explain why Frida’s method will not solve the equation.Emiliano thinks x=40 is the solution to the equation 12x=80 . Explain why he is wrong.Solve: 3x+4=8 .Solve: 5a+3=37 .Solve: 5y9=16 .Solve: 3m8=19 .Solve: 6n=5n10 .Solve: 6c=7c1 .Solve: 3p14=5p .Solve: 8m+9=5m .Solve: 12j=4j+32 .Solve: 8h=4h+12 .Solve: 12x+8=6x+2 .Solve: 9y+4=7y+12 .Solve: 8q5=4q+7 .Solve: 7n3=n+3 .Solve: 2a2=6a+18 .Solve: 4k1=7k+17 .Solve: 78x12=18x2 .Solve: 76y+11=16y+8 .Solve: 2.8x+12=1.4x9 .Solve: 3.6y+8=1.2y4 .In the following exercises, solve the following equations with constants on both sides. 174. 9x3=60 In the following exercises, solve the following equations with constants on both sides. 175. 12x8=64 In the following exercises, solve the following equations with constants on both sides. 176. 14w+5=117 In the following exercises, solve the following equations with constants on both sides. 177. 15y+7=97 In the following exercises, solve the following equations with constants on both sides. 178. 2a+8=28 In the following exercises, solve the following equations with constants on both sides. 179. 3m+9=15 In the following exercises, solve the following equations with constants on both sides. 180. 62=8n6 In the following exercises, solve the following equations with constants on both sides. 181. 77=9b5 In the following exercises, solve the following equations with constants on both sides. 182. 35=13y+9 In the following exercises, solve the following equations with constants on both sides. 183. 60=21x24 In the following exercises, solve the following equations with constants on both sides. 184. 12p9=9 In the following exercises, solve the following equations with constants on both sides. 185. 14q2=16 In the following exercises, solve the following equations with variables on both sides. 186. 19z=18z7 In the following exercises, solve the following equations with variables on both sides. 187. 21k=20k11 In the following exercises, solve the following equations with variables on both sides. 188. 9x+36=15x In the following exercises, solve the following equations with variables on both sides. 189. 8x+27=11x In the following exercises, solve the following equations with variables on both sides. 190. c=3c20 In the following exercises, solve the following equations with variables on both sides. 191. b=4b15 In the following exercises, solve the following equations with variables on both sides. 192. 9q=442q In the following exercises, solve the following equations with variables on both sides. 193. 5z=398z In the following exercises, solve the following equations with variables on both sides. 194. 6y+12=5y In the following exercises, solve the following equations with variables on both sides. 195. 4x+34=3x In the following exercises, solve the following equations with variables on both sides. 196. 18a8=22a In the following exercises, solve the following equations with variables on both sides. 197. 11r8=7r In the following exercises, solve the following equations with variables and constants on both sides. 198. 8x15=7x+3 In the following exercises, solve the following equations with variables and constants on both sides. 199. 6x17=5x+2 In the following exercises, solve the following equations with variables and constants on both sides. 200. 26+13d=14d+11 In the following exercises, solve the following equations with variables and constants on both sides. 201. 21+18f=19f+14 In the following exercises, solve the following equations with variables and constants on both sides. 202. 2p1=4p33 In the following exercises, solve the following equations with variables and constants on both sides. 203. 12q5=9q20 In the following exercises, solve the following equations with variables and constants on both sides. 204. 4a+5=a40 In the following exercises, solve the following equations with variables and constants on both sides. 205. 8c+7=3c37 In the following exercises, solve the following equations with variables and constants on both sides. 206. 5y30=5y+30 In the following exercises, solve the following equations with variables and constants on both sides. 207. 7x17=8x+13 In the following exercises, solve the following equations with variables and constants on both sides. 208. 7s+12=5+4s In the following exercises, solve the following equations with variables and constants on both sides. 209. 9p+14=6+4p In the following exercises, solve the following equations with variables and constants on both sides. 210. 2z6=23z In the following exercises, solve the following equations with variables and constants on both sides. 211. 3y4=12y In the following exercises, solve the following equations with variables and constants on both sides. 212. 53c3=23c16 In the following exercises, solve the following equations with variables and constants on both sides. 213. 74m7=34m13 In the following exercises, solve the following equations with variables and constants on both sides. 214. 825q=35q+6 In the following exercises, solve the following equations with variables and constants on both sides. 215. 1115a=45a+4 In the following exercises, solve the following equations with variables and constants on both sides. 216. 43n+9=13n9 In the following exercises, solve the following equations with variables and constants on both sides. 217. 54a+15=34a5 In the following exercises, solve the following equations with variables and constants on both sides. 218. 14y+7=34y3 In the following exercises, solve the following equations with variables and constants on both sides. 219. 35p+2=45p1 In the following exercises, solve the following equations with variables and constants on both sides. 220. 14n+8.25=9n+19.60 In the following exercises, solve the following equations with variables and constants on both sides. 221. 13z+6.45=8z+23.75 In the following exercises, solve the following equations with variables and constants on both sides. 222. 2.4w100=0.8w+28 In the following exercises, solve the following equations with variables and constants on both sides. 223. 2.7w80=1.2w+10 In the following exercises, solve the following equations with variables and constants on both sides. 224. 5.6r+13.1=3.5r+57.2 In the following exercises, solve the following equations with variables and constants on both sides. 225. 6.6x18.9=3.4x+54.7 Concert tickets At a school concert the total value of tickets sold was $1506. Student tickets sold for $6 and adult tickets sold for $9. The number of adult tickets sold was 5 less than 3 times the number of student tickets. Find the number of student tickets sold, s, by solving the equation 6s+27s45=1506 .Making a fence Jovani has 150 feet of fencing to make a rectangular garden in his backyard. He wants the length to be 15 feet more than the width. Find the width, w, by solving the equation 150=2w+30+2w .Solve the equation 65y815y+7 explaining all the steps of your solution as in the examples in this section.Solve the equation 10x+14=2x+38 explaining all the steps of your solution as in the examples in this section.When solving an equation with variables on both sides, why is it usually better to choose the side with the larger coefficient of x to be the “variable” side?Is x=2 a solution to the equation 52x=4x+1 ? How do you know?Solve: 5(x+3)=35 .Solve: 6(y4)=18 .Solve: (y+8)=2 .Solve: (z+4)=12 .Solve: 2(m4)+3=1 .Solve: 7(n3)8=15 .Solve: 13(6u+3)=7u .Solve: 23(9x12)=8+2x .Solve: 123(4j+3)=17 .Solve: 68(k2)=10 .Solve: 6(p3)7=5(4p+3)12 .Solve: 8(q+1)5=3(2q4)1 .Solve: 6[42(7y1)]=8(138y) .Solve: 12[15(4z1)]=3(24+11z) .Solve: 0.55(100n+8)=0.6(85n+14) .Solve: 0.15(40m120)=0.5(60m+12) .Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: 4+9(3x7)=42x13+23(3x2)Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: 8(13x)+15(2x+7)=2(x+50)+4(x+3)+1 Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: 11(q+3)5=19 Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: 6+14(k8)=95 Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: 12c+5(5+3c)=3(9c4)Classify the equation as a conditional equation, an identity, or a contradiction and then state the solution: 4(7d+18)=13(3d2)11d In the following exercises, solve each linear equation. 232. 15(y9)=60 In the following exercises, solve each linear equation. 233. 21(y5)=42 In the following exercises, solve each linear equation. 234. 9(2n+1)=36 In the following exercises, solve each linear equation. 235. 16(3n+4)=32 In the following exercises, solve each linear equation. 236. 8(22+11r)=0 In the following exercises, solve each linear equation. 237. 5(8+6p)=0 In the following exercises, solve each linear equation. 238. (w12)=30 In the following exercises, solve each linear equation. 239. (t19)=28 In the following exercises, solve each linear equation. 240. 9(6a+8)+9=81 In the following exercises, solve each linear equation. 241. 8(9b4)12=100 In the following exercises, solve each linear equation. 242. 32+3(z+4)=41 In the following exercises, solve each linear equation. 243. 21+2(m4)=25 In the following exercises, solve each linear equation. 244. 51+5(4q)=56 In the following exercises, solve each linear equation. 245. 6+6(5k)=15 In the following exercises, solve each linear equation. 246. 2(9s6)62=16 In the following exercises, solve each linear equation. 247. 8(6t5)35=27 In the following exercises, solve each linear equation. 248. 3(102x)+54=0 In the following exercises, solve each linear equation. 249. 2(117x)+54=4 In the following exercises, solve each linear equation. 250. 23(9c3)=22 In the following exercises, solve each linear equation. 251. 35(10x5)=27 In the following exercises, solve each linear equation. 252. 15(15c+10)=c+7 In the following exercises, solve each linear equation. 253. 14(20d+12)=d+7 In the following exercises, solve each linear equation. 254. 18(9r+7)=16 In the following exercises, solve each linear equation. 255.Y1 15(3r+8)=28 In the following exercises, solve each linear equation. 256. 5(n1)=19 In the following exercises, solve each linear equation. 257. 3(m1)=13 In the following exercises, solve each linear equation. 258. 114(y8)=43 In the following exercises, solve each linear equation. 259. 182(y3)=32 In the following exercises, solve each linear equation. 260. 248(3v+6)=0 In the following exercises, solve each linear equation. 261. 355(2w+8)=10 In the following exercises, solve each linear equation. 262. 4(a12)=3(a+5)In the following exercises, solve each linear equation. 263. 2(a6)=4(a3)In the following exercises, solve each linear equation. 264. 2(5u)=3(2u+6)In the following exercises, solve each linear equation. 265. 5(8r)=2(2r16)In the following exercises, solve each linear equation. 266. 3(4n1)2=8n+3 In the following exercises, solve each linear equation. 267. 9(2m3)8=4m+7 In the following exercises, solve each linear equation. 268. 12+2(53y)=9(y1)2 In the following exercises, solve each linear equation. 269. 15+4(25y)=7(y4)+4 In the following exercises, solve each linear equation. 270. 8(x4)7x=14 In the following exercises, solve each linear equation. 271. 5(x4)4x=14 In the following exercises, solve each linear equation. 272. 5+6(3s5)=3+2(8s1)In the following exercises, solve each linear equation. 273. 12+8(x5)=4+3(5x2)In the following exercises, solve each linear equation. 274. 4(u1)8=6(3u2)7 In the following exercises, solve each linear equation. 275. 7(2n5)=8(4n1)9 In the following exercises, solve each linear equation. 276. 4(p4)(p+7)=5(p3)In the following exercises, solve each linear equation. 277. 3(a2)(a+6)=4(a1)In the following exercises, solve each linear equation. 278. 9(9y+5)3(3y7)=16(4y2)In the following exercises, solve each linear equation. 279. (7m+4)(2m5)=14(5m3)In the following exercises, solve each linear equation. 280. 4[58(4c3)]=12(113c)8 In the following exercises, solve each linear equation. 281. 5[92(6d1)]=11(410d)139 In the following exercises, solve each linear equation. 282. 3[9+8(4h3)]=2(512h)19 In the following exercises, solve each linear equation. 283. 3[14+2(15k6)]=8(35k)24 In the following exercises, solve each linear equation. 284. 5[2(m+4)+8(m7)]=2[3(5+3)(213m)]In the following exercises, solve each linear equation. 285. 10[5(n+1)+4(n1)]=11[7(5+n)(253n)]In the following exercises, solve each linear equation. 286. 5(1.2u4.8)=12 In the following exercises, solve each linear equation. 287. 4(2.5v0.6)=7.6 In the following exercises, solve each linear equation. 288. 0.25(q6)=0.1(q+18)In the following exercises, solve each linear equation. 289. 0.2(p6)=0.4(p+14)In the following exercises, solve each linear equation. 290. 0.2(30n+50)=28 In the following exercises, solve each linear equation. 291. 0.5(16m+34)=15 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 292. 23z+19=3(5z9)+8z+46 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 293. 15y+32=2(10y7)5y+46 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 294. 5(b9)+4(3b+9)=6(4b5)7b+21 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 295. 9(a4)+3(2a+5)=7(3a44)6a+7 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 296. 18(5j1)+29=47 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 297. 24(3d4)+100=52 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 298. 22(3m4)=8(2m+9)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 299. 30(2n1)=5(10n+8)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 300. 7v+42=11(3v+8)2(13v1)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 301. 18u51=9(4u+5)6(3u10)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 302. 3(6q9)+7(q+4)=5(6q+8)5(q+1)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 303. 5(p+4)+8(2p1)=9(3p5)6(p2)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 304. 12(6h1)=8(8h+5)4 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 305. 9(4k7)=11(3k+1)+4 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 306. 45(3y2)=9(15y6)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 307. 60(2x1)=15(8x+5)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 308. 16(6n+15)=48(2n+5)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 309. 36(4m+5)=12(12m+15)In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 310. 9(14d+9)+4d=13(10d+6)+3 In the following exercises, classify each equation as a conditional equation, an identity, or a contradiction and then state the solution. 311. 11(8c+5)8c=2(40c+25)+5 Fencing Micah has 44 feet of fencing to make a dog run in his yard. He wants the length to be 2.5 feet more than the width. Find the length, L, by solving the equation 2L+2(L2.5)=44 .Coins Rhonda has $1.90 in nickels and dimes. The number of dimes is one less than twice the number of nickels. Find the number of nickels, n, by solving the equation 0.05n+0.10(2n1)=1.90 .Using your own words, list the steps in the general strategy for solving linear equations.Explain why you should simplify both sides of an equation as much as possible before collecting the variable terms to one side and the constant terms to the other side.What is the first step you take when solving the equation 37(y4)=38 ? Why is this your first step?Solve the equation 14(8x+20)=3x4 explaining all the steps of your solution as in the examples in this section.Solve: 14x+12=58 .Solve: 18x+12=14 .Solve: 7=12x+34x23x .Solve: 1=12u+14u23u .Solve: x+13=16x12 .Solve: c+34=12c14 .Solve: 11=12(6p+2) .Solve: 8=13(9q+6) .Solve: 15(n+3)=14(n+2) .Solve: 12(m3)=14(m7) .Solve: 4y73=y6 .Solve: 2z54=z8 .Solve: b10+2=b4+5 .Solve: c6+3=c3+4 .Solve: 3r+56+1=4r+33 .Solve: 2s+32+1=3s+24 .Solve: 0.14h+0.12=0.35h2.4 .Solve: 0.65k0.1=0.4k0.35 .Solve: 0.25n+0.05(n+5)=2.95 .Solve: 0.10d+0.05(d5)=2.15 .In the following exercises, solve each equation with fraction coefficients. 318. 14x12=34 In the following exercises, solve each equation with fraction coefficients. 319. 34x12=14 In the following exercises, solve each equation with fraction coefficients. 320. 56y23=32 In the following exercises, solve each equation with fraction coefficients. 321. 56y13=76 In the following exercises, solve each equation with fraction coefficients. 322. 12a+38=34 In the following exercises, solve each equation with fraction coefficients. 323. 58b+12=34 In the following exercises, solve each equation with fraction coefficients. 324. 2=13x12x+23x In the following exercises, solve each equation with fraction coefficients. 325. 2=35x13x+25x In the following exercises, solve each equation with fraction coefficients. 326. 14m45m+12m=1 In the following exercises, solve each equation with fraction coefficients. 327. 56n14n12n=2 In the following exercises, solve each equation with fraction coefficients. 328. x+12=23x12 In the following exercises, solve each equation with fraction coefficients. 329. x+34=12x54 In the following exercises, solve each equation with fraction coefficients. 330. 13w+54=w14 In the following exercises, solve each equation with fraction coefficients. 331. 32z+13=z23 In the following exercises, solve each equation with fraction coefficients. 332. 12x14=112x+16 In the following exercises, solve each equation with fraction coefficients. 333. 12a14=16a+112

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