Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Elementary Algebra
Add: 1130+712 .Add: 38+920 .Add: 215a2b+56ab2 .Add: 516c+38cd2 .Add: 2x2+5x+3 .Add: 4m+3+3m+4 .Add: 5xxyy2+2xx2+y2 .Add: 72m+6+4m2+4m+3 .Add: 1m2m2+5mm2+3m+2 .Add: 2nn23n10+6n2+5n+6 .Subtract: yy+4y2y5 .Subtract: z+3z+2zz+3 .Subtract: 2xx241x+2 .Subtract: 3z+36zz29 .Subtract: 3x1x25x626x .Subtract: 2y2y2+2y8y12y .Subtract: 2x+1x73 .Subtract: 4y+32y15Simplify: vv+1+3v16v21 .Simplify: 3ww+2+2w+717w+4w2+9w+14 .In the following exercises, find the LCD. 169. 5x22x8,2xx2x12In the following exercises, find the LCD. 170. 8y2+12y+35,3yy2+y42In the following exercises, find the LCD. 171. 9z2+2z8,4zz24In the following exercises, find the LCD. 172. 6a2+14a+45,5aa281In the following exercises, find the LCD. 173. 4b2+6b+9,2bb22b15the following exercises, find the LCD. 174. 5c24c+4,3cc210c+16In the following exercises, find the LCD. 175. 23d2+14d5,5d3d219d+6In the following exercises, find the LCD. 176. 35m23m2,6m5m2+17m+6In the following exercises, write as equivalent rational expressions with the given LCD. 177. 5x22x8,2xx2x12 LCD (x4)(x+2)(x+3)In the following exercises, write as equivalent rational expressions with the given LCD. 178. 8y2+12y+35,3yy2+y42 LCD (y+7)(y+5)(y6)In the following exercises, write as equivalent rational expressions with the given LCD. 179. 9z2+2z8,4zz24 LCD (z2)(z+4)(z+2)In the following exercises, write as equivalent rational expressions with the given LCD. 180. 6a2+14a+45,5aa281 LCD (a+9)(a+5)(a9)In the following exercises, write as equivalent rational expressions with the given LCD. 181. 4b2+6b+9,2bb22b15 LCD (b+3)(b+3)(b5)In the following exercises, write as equivalent rational expressions with the given LCD. 182. 5c24c+4,3cc210c+10 LCD (c2)(c2)(c8)In the following exercises, write as equivalent rational expressions with the given LCD. 183. 23d2+14d5,2d3d219d+6 LCD (3d1)(d+5)(d6)In the following exercises, write as equivalent rational expressions with the given LCD. 184. 35m23m2,6m5m2+17m+6 LCD (5m+2)(m1)(m+3)In the following exercises, add. 185. 524+1136In the following exercises, add. 186. 730+1345In the following exercises, add. 187. 920+1130In the following exercises, add. 188. 827+718In the following exercises, add. 189. 710x2y+415xy2In the following exercises, add. 190. 112a3b2+59a2b3In the following exercises, add. 191. 12m+78m2nIn the following exercises, add. 192. 56p2q+14pIn the following exercises, add. 193. 3r+4+2r5In the following exercises, add. 194. 4s7+5s+3In the following exercises, add. 195. 8t+5+6t5In the following exercises, add. 196. 7v+5+9v5In the following exercises, add. 197. 53w2+2w+1In the following exercises, add. 198. 42x+5+2x1In the following exercises, add. 199. 2yy+3+3y1In the following exercises, add. 200. 3zz2+1z+5In the following exercises, add. 201. 5ba2b2a2+2bb24In the following exercises, add. 202. 4cd+3c+1d29In the following exercises, add. 203. 2m3m3+5mm2+3m4In the following exercises, add. 204. 34n+4+6n2n2In the following exercises, add. 205. 3n2+3n18+4nn2+8n+12In the following exercises, add. 206. 6q23q10+5qq28q+15In the following exercises, add. 207. 3rr2+7r+6+9r2+4r+3In the following exercises, add. 208. 2ss2+2s8+4s2+3s10In the following exercises, subtract. 209. tt6t2t+6In the following exercises, subtract. 210. vv3v6v+1In the following exercises, subtract. 211. w+2w+4ww2In the following exercises, subtract. 212. x3x+6xx+3In the following exercises, subtract. 213. y4y+11y+7In the following exercises, subtract. 214. z+8z3zz2In the following exercises, subtract. 215. 5aa+3a+2a+6In the following exercises, subtract. 216. 3bb2b6b8In the following exercises, subtract. 217. 6cc2253c+5In the following exercises, subtract. 218. 4dd2812d+9In the following exercises, subtract. 219. 6m+612mm236In the following exercises, subtract. 220. 4n+48nn216In the following exercises, subtract. 221. 9p17p24p21p+17pIn the following exercises, subtract. 222. 7q+8q22q24q+24qIn the following exercises, subtract. 223. 2r16r2+6r1652rIn the following exercises, subtract. 224. 2t30t2+6r1623tIn the following exercises, subtract. 225. 5v2v+34In the following exercises, subtract. 226. 6w+5w1+2In the following exercises, subtract. 227. 2x+710x1+3In the following exercises, subtract. 228. 8y45y+26In the following exercises, add and subtract. 229. 5aa2+9a2a+18a22aIn the following exercises, add and subtract. 230. 2bb5+32b2b152b210bIn the following exercises, add and subtract. 231. cc+2+5c211cc24In the following exercises, add and subtract. 232. 6dd5+1d+47d5d2d20In the following exercises, simplify. 233. 6a3ab+b2+3a9a2b2In the following exercises, simplify. 234. 2c2c+10+7cc2+9c+20In the following exercises, simplify. 235. 6dd2643d8In the following exercises, simplify. 236. 5n+710nn249In the following exercises, simplify. 237. 4mm2+6m7+2m2+10m+21In the following exercises, simplify. 238. 3pp2+4p12+1p2+p30In the following exercises, simplify. 239. 5n5n2+n6+n+12nIn the following exercises, simplify. 240. 4b24b2+b30+b+75bIn the following exercises, simplify. 241. 715p+518pqIn the following exercises, simplify. 242. 320a2+1112ab2In the following exercises, simplify. 243. 4x2+3x+5In the following exercises, simplify. 244. 6m+4+9m8In the following exercises, simplify. 245. 2q+7y+42In the following exercises, simplify. 246. 3y1y+42In the following exercises, simplify. 247. z+2z5zz+1In the following exercises, simplify. 248. tt5t1t+5In the following exercises, simplify. 249. 3dd+2+4dd+8d2+2dIn the following exercises, simplify. 250. 2qq+5+3q313q+15q2+2q15Decorating cupcakes Victoria can decorate an order of cupcakes for a wedding in t hours, so in 1 hour she can decorate 1t of the cupcakes. It would take her sister 3 hours longer to decorate the same order of cupcakes, so in 1 hour she can decorate 1t+3 of the cupcakes. a. Find the fraction of the decorating job that Victoria and her sister, working together, would complete in one hour by adding the rational expressions 1t+1t+3 . b. Evaluate your answer to part (a) when t=5Kayaking When Trina kayaks upriver, it takes her 53c hours to go 5 miles, where c is the speed of the river current. It takes her 53+c hours to kayak 5 miles down the river. a. Find an expression for the number of hours it would take Trina to kayak 5 miles up the river and then return by adding 53c+53+c b. Evaluate your answer to part (a) when c = 1 to find the number of hours it would take Trina if the speed of the river current is 1 mile per hour.Felipe thinks 1x+1y is 2x+y . a. Choose numerical values for x and y and evaluate 1x+1y . b. Evaluate 2x+y for the same values of x and y you used in part (a). c. Explain why Felipe is wrong. d. Find the correct expression for 1x+1y .Simplify the expression 4n2+6n+91n29 and explain all your steps.Simplify: 2x213x+1 .Simplify: 1x27x+122x4 .Simplify: 12+2356+112 .Simplify: 341318+56 .Simplify: 1x+1y1x1y .Simplify: 1a+1b1a21b2 .Simplify: b3bb+52b+5+1b5 .Simplify: 13c+41c+4+c3 .Simplify: 12+15110+15 .Simplify: 14+3812516 .Simplify: 1a+1babba .Simplify: 1x21y21x+1y .Simplify: 3x+25x2+3x24 .Simplify: 2x71x+76x+71x249 .Simplify: 3x2+7x+104x+2+1x+5Simplify: 4yy+5+2y+63yy2+11y+30 .Simplify: xx+31+1x+3 .Simplify: 1+1x13x+1 .In the following exercises, simplify. 255. 2aa+44a2a216In the following exercises, simplify. 256. 3bb5b2b225In the following exercises, simplify. 257. 5c2+5c1410c+7In the following exercises, simplify. 258. 8d2+9d+1812d+6In the following exercises, simplify. 259. 12+5623+79 sIn the following exercises, simplify. 260. 12+3435+710In the following exercises, simplify. 261. 231934+56In the following exercises, simplify. 262. 121623+34In the following exercises, simplify. 263. nm+1n1nnmIn the following exercises, simplify. 264. 1p+pqqp1qIn the following exercises, simplify. 265. 1r+1t1r21r2In the following exercises, simplify. 266. 2v+2w1v21w2In the following exercises, simplify. 267. x2xx+31x+3+1x3In the following exercises, simplify. 268. y2yy42y42y+4In the following exercises, simplify. 269. 22a+31a+3+a2In the following exercises, simplify. 270. 44b51b5+b4In the following exercises, simplify. 271. 13+1814+112In the following exercises, simplify. 272. 14+1916+112In the following exercises, simplify. 273. 56+2971813In the following exercises, simplify. 274. 16+4153512In the following exercises, simplify. 275. cd+1d1ddcIn the following exercises, simplify. 276. 1m+mnnm1nIn the following exercises, simplify. 277. 1p+1q1p21q2In the following exercises, simplify. 278. 2r+2t1r21t2In the following exercises, simplify. 279. 2x+53x5+1x225In the following exercises, simplify. 280. 5y43y+4+2y216In the following exercises, simplify. 281. 5x264+3z+81z+8+2z8In the following exercises, simplify. 282. 3s+6+5s61s236+4s+6In the following exercises, simplify. 283. 4a22a151a5+2a+3In the following exercises, simplify. 284. 5b26b273b9+1b+3In the following exercises, simplify. 285. 5c+23c+75cc2+9c+14In the following exercises, simplify. 286. 6d42d+72dd2+3d28In the following exercises, simplify. 287. 2+1p35p3In the following exercises, simplify. 288. nn23+5n2In the following exercises, simplify. 289. mm+54+1m5In the following exercises, simplify. 290. 7+1q21q+2In the following exercises, use either method. 291. 342712+514In the following exercises, use either method. 292. vw+1v1vvwIn the following exercises, use either method. 293. 2a+41a216In the following exercises, use either method. 294. 3b23b402b+52b8In the following exercises, use either method. 295. 3m+3n1m21n2In the following exercises, use either method. 296. 2r91r+9+3r281In the following exercises, use either method. 297. x3xx+23x+2+3x2In the following exercises, use either method. 298. yy+32+1y3Electronics The resistance of a circuit formed by connecting two resistors in parallel is 11R1+1R2 . a. Simplify the complex fraction 11R1+1R2 . ® Find the resistance of the circuit when R1=8 and R2=12Ironing Lenore can do the ironing for her family’s business in h hours. Her daughter would take h+2 hours to get the ironing done. If Lenore and her daughter work together, using 2 irons, the number of hours it would take them to do all the ironing is 11h+1h+2 .a. Simplify the complex fraction 11h+1h+2 . b. Find the number of hours it would take Lenore and her daughter, working together, to get the ironing done if h=4 .In this section, you learned to simplify the complex fraction 3x+2x x 2 4 two ways: rewriting it as a division problem multiplying the numerator and denominator by the LCD Which method do you prefer? Why?Efraim wants to start simplifying the complex fraction 1a+1b1a1b by cancelling the variables from the numerator and denominator. Explain what is wrong with Efraim’s plan.Solve: 1y+23=15 .Solve: 23+15=1x .Solve: 12a=15a2 .Solve: 14b=12b2 .Solve: 1x1=23x .Solve: 35n+1=23n .Solve: 2x+1+1x1=1x21 .Solve: 5y+3+2y3=5y29 .Solve: 2x+51x1=1 .Solve: 3x+82x2=1 .Solve: x+13x27x+10=6x54x2 .Solve: y14y2+3y4=2y+4+7y1 .Solve: x18+x+69x=23x .Solve: y+55y+y15=1y .Solve: xx+4=32x216+5 .Solve: yy+8=128y264+9 .Solve: y5y1053y+6=2y219y+5415y260 .Solve: z2z+834z8=3z216z68z2+8z64 .Solve: AL=W for L.Solve: FA=W for A.Solve: y2x+1=23 for x.Solve: x=y1y for y.Solve: 1a+1b=c for a.Solve: 2x+13=1y for y.In the following exercises, solve. 303. 1a+25=12In the following exercises, solve. 304. 56+3b=13In the following exercises, solve. 305. 521c=34In the following exercises, solve. 306. 632d=49In the following exercises, solve. 307. 45+14=2vIn the following exercises, solve. 308. 37+23=1wIn the following exercises, solve. 309. 79+1x=23In the following exercises, solve. 310. 38+2y=14In the following exercises, solve. 311. 12m=8m2In the following exercises, solve. 312. 1+4n=21n2In the following exercises, solve. 313. 1+9p=20p2In the following exercises, solve. 314. 17q=6q2In the following exercises, solve. 315. 1r+3=42rIn the following exercises, solve. 316. 3t6=1tIn the following exercises, solve. 317. 53v2=74vIn the following exercises, solve. 318. 82w+1=3wIn the following exercises, solve. 319. 3x+4+7x4=8x216In the following exercises, solve. 320. 5y9+7y+9=18y281In the following exercises, solve. 321. 8z10+7z+10=5z2100In the following exercises, solve. 322. 9a+11+6a11=7a2121In the following exercises, solve. 323. 1q+47q2=1In the following exercises, solve. 324. 3r+104r4=1In the following exercises, solve. 325. 1t+75t5=1In the following exercises, solve. 326. 2s+73s3=1In the following exercises, solve. 327. v10v25v+4=3v16v4In the following exercises, solve. 328. w+8w211w+28=5w7+2w4In the following exercises, solve. 329. x10x2+8x+12=3x+2+4x+6In the following exercises, solve. 330. y3y24y5=1y+1+8y5In the following exercises, solve. 331. z16+z+24z=12zIn the following exercises, solve. 332. a9+a+33a=1aIn the following exercises, solve. 333. b+33b+b24=1bIn the following exercises, solve. 334. c+312c+c36=14cIn the following exercises, solve. 335. dd+3=18d29+4In the following exercises, solve. 336. mm+5=50m225+6In the following exercises, solve. 337. nn+2=8m24+3In the following exercises, solve. 338. pp+7=98p249+8In the following exercises, solve. 339. q3q934q+12=7q2+6q+6324q2216In the following exercises, solve. 340. r3r1514r+20=3r2+17r+4012r2300In the following exercises, solve. 341. s2s+625s+5=5s23s710s2+40s+30In the following exercises, solve. 342. t6t1252t+10=t223t+7012t2+36t120In the following exercises, solve. 343. Cr=2 for rIn the following exercises, solve. 344. Ir=P for rIn the following exercises, solve. 345. Vh=lw for hIn the following exercises, solve. 346. 2Ab=h for bIn the following exercises, solve. 347. v+3w1=12 for wIn the following exercises, solve. 348. x+52y=43 for yIn the following exercises, solve. 349. a=b+3c2 for cIn the following exercises, solve. 350. m=n2n for nIn the following exercises, solve. 351. 1p+2q=4 for pIn the following exercises, solve. 352. 3s+1t=2 for sIn the following exercises, solve. 353. 2v+15=12 for vIn the following exercises, solve. 354. 6x+23=1y for yIn the following exercises, solve. 354. m+3n2=45 for nIn the following exercises, solve. 356. Ec=m2 for cIn the following exercises, solve. 357. 3x5y=14 for yIn the following exercises, solve. 358. RT=W for TIn the following exercises, solve. 359. r=s3t for tIn the following exercises, solve. 360. c=2a+b5 for aHouse Painting Alain can paint a house in 4 days. Spiro would take 7 days to paint the same house. Solve the equation 14+17=1t for t to find the number of days it would take them to paint the house if they worked togetherBoating An can drive his boat 18 miles with the current in the same amount of time it takes to drive 10 miles against the current. If the speed of the boat is 7 knots, solve the equation 187+c=107c for c to find the speed of the current.Why is there no solution to the equation 3x2=5x2 ?Pete thinks the equation yy+6=72y236+4 has two solutions, y=6 and y=4 . Explain why Pete is wrong.Solve the proportion: n84=1112 .Solve the proportion: y96=1312 .Solve the proportion: 91b=75 .Solve the proportion: 39c=138 .Solve the proportion: yy+55=38 .Solve the proportion: zz84=15 .Solve : v+308=v+6612 .Solve: 2x+159=7x+315 .Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Emilia, who weighs 60 pounds?For every 1 kilogram (kg) of a child’s weight pediatricians prescribe 15 milligrams (mg) of a fever reducer. If Isabella weighs 12 kg, how many milligrams of the fever reducer will the pediatrician prescribe?At a fast-food restaurant, a 22-ounce chocolate shake has 850 calories. I-low many calories are in their 12-ounce chocolate shake? Round your answer to nearest whole number.Yaneli loves Starburst candies, but wants to keep her snacks to 100 calories. If the candles have 160 calories for 8 pieces, how many pieces can she have in her snack?yurianna is going to Europe and wants to change $800 dollars into Euros. At the current exchange rate, $1 US is equal to 0.738 Euro. How many Euros will she have for her trip?Corey and Nicole are traveling to Japan and need to exchange $600 into Japanese yen. It each dollar is 94.1 yen, how many yen will they get?ABC is similar to XYZ The lengths of two sides of each triangle are given in the figure. Find the length of side a.ABC is similar to XYZ. The lengths of two sides of each triangle are given in the figure. Find the length of side y.On the map, Seattle. Portland, and Boise form a triangle whose sides are shown in the figure below. If the actual distance from Seattle to Boise is 400 miles, find the distance from Seattle to Portland.Using the map above, find the distance from Portland to Boise.A telephone pole casts a shadow that s 50 feet long. Nearby, an 8 foot tall traffic sign casts a shadow that is 10 feet long. How tall is the telephone pole?A pine tree casts a shadow of 80 feet next to a 30-foot tall building which casts a 40 feet shadow. How tall is the pine tree?In the following exercises, solve. 365. x56=78In the following exercises, solve. 366. n91=813In the following exercises, solve. 367. 4963=z9In the following exercises, solve. 368. 5672=y9In the following exercises, solve. 369. 5a=65117In the following exercises, solve. 370. 4b=64144In the following exercises, solve. 371. 98154=7pIn the following exercises, solve. 372. 72156=6qIn the following exercises, solve. 373. a8=4248In the following exercises, solve. 374. b7=3042In the following exercises, solve. 375. 2.7j=0.90.2In the following exercises, solve. 376. 2.8k=2.11.5In the following exercises, solve. 377. aa+12=47In the following exercises, solve. 278. bb16=119In the following exercises, solve. 379. cc104=58In the following exercises, solve. 380. dd48=133In the following exercises, solve. 381. m+9025=m+3015In the following exercises, solve. 382. n+104=40n6In the following exercises, solve. 383. 2p+48=p+186In the following exercises, solve. 384. q22=2q718In the following exercises, solve. 385. Pediatricians prescribe 5 milliliters (ml) of acetaminophen for every 25 pounds of a child’s weight. How many milliliters of acetaminophen will the doctor prescribe for Jocelyn, who weighs 45 pounds?In the following exercises, solve. 386. Brianna, who weighs 6 kg, just received her shots and needs a pain killer. The pain killer is prescribed for children at 15 milligrams (mg) for every 1 kilogram (kg) of the child’s weight. How many milligrams will the doctor prescribe?