Prealgebra (6th Edition)
Prealgebra (6th Edition)
6th Edition
ISBN: 9780134179018
Author: Jamie Blair, John Tobey Jr., Jeffrey Slater, Jenny Crawford
Publisher: PEARSON
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Chapter 6.1, Problem 54E

Determine the value of a if x ≠ 0 .

( a x − 5 ) + ( 4 x 2 + 6 x + 9 ) + ( 3 x − 1 ) = 4 x 2 − 2 x + 3

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Chapter 6 Solutions

Prealgebra (6th Edition)

Ch. 6.1 - Fill in the blanks. To subtract two polynomials,...Ch. 6.1 - Fill in the blanks. To add two polynomials, we...Ch. 6.1 - Identify the terms of each polynomial. 5a26a+2b4+1Ch. 6.1 - Identify the terms of each polynomial....Ch. 6.1 - Identify the terms of each polynomial. 6x63x33y1Ch. 6.1 - Identify the terms of each polynomial. 2y33x24z38Ch. 6.1 - Perform the operations indicated. (7y3)+(4y+9)Ch. 6.1 - Perform the operations indicated. (2x3)+(7x+6)Ch. 6.1 - Perform the operations indicated. (2a23a+6)+(4a2)Ch. 6.1 - Perform the operations indicated. (3c26c+3)+(2c7)
Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Simplify. (5x+2y)Ch. 6.1 - Simplify. (8x+5y)Ch. 6.1 - Simplify. (8x+4)Ch. 6.1 - Simplify. (5a+3)Ch. 6.1 - Simplify. (3x+6z5y)Ch. 6.1 - Simplify. (3x+4y8z)Ch. 6.1 - Perform the operations indicated. (10x+7)(3x+5)Ch. 6.1 - Perform the operations indicated. (8x+7)(3a+2)Ch. 6.1 - Perform the operations indicated. (7x3)(4x+6)Ch. 6.1 - Perform the operations indicated. (5y+2)(7y8)Ch. 6.1 - Perform the operations indicated. (8a+5)(4a3)Ch. 6.1 - Perform the operations indicated. (5c+2)(3c6)Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated. (4x2+7x+1)(x25)Ch. 6.1 - Perform the operations indicated. (3x2+7x+2)(x22)Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Perform the operations indicated....Ch. 6.1 - Determine the value of a if x0....Ch. 6.1 - Determine the value of a if x0....Ch. 6.1 - Determine the values of a and b if x0....Ch. 6.1 - Determine the values of a and b if x0....Ch. 6.1 - Perform the operation indicated. [4.4.1] 6x82x2Ch. 6.1 - Perform the operation indicated. [4.4.1]...Ch. 6.1 - Perform the operation indicated. [3.4.2] (4x)(2x2)Ch. 6.1 - Perform the operation indicated. [3.4.2]...Ch. 6.1 - [5.6.1]Miles Walked Maria walked 227 miles and...Ch. 6.1 - [5.6.1]Recipe Mixture A cook mixed 37 cup of brown...Ch. 6.1 - Perform the operations indicated. a. (3x+1)+(5x2)...Ch. 6.1 - Perform the operations indicated. a. (6a4)(3a2) b....Ch. 6.1 - Perform the operations indicated. a....Ch. 6.1 - Concept Check Mitchell subtracted two polynomials...Ch. 6.2 - Erin multiplied (4)(x2+2x+1) and obtained this...Ch. 6.2 - Write in words the multiplication that the word...Ch. 6.2 - Fill in the blanks and boxes to complete each...Ch. 6.2 - Fill in the blanks and boxes to complete each...Ch. 6.2 - Multiply. 3(3y24y+2) First term of the product is:...Ch. 6.2 - Multiply. 2(3y26y+1) First term of the product is:...Ch. 6.2 - To multiply (x1)(x2+3x+1): We multiply x times the...Ch. 6.2 - To multiply (y2)(y2+4y+3): We multiply the...Ch. 6.2 - Prob. 9ECh. 6.2 - Prob. 10ECh. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply. 3x2(x2)Ch. 6.2 - Use the distributive property to multiply. 4x3(x3)Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use the distributive property to multiply....Ch. 6.2 - Use FOIL to multiply. (x+6)(x+7)Ch. 6.2 - Use FOIL to multiply. (a+2)(a+1)Ch. 6.2 - Use FOIL to multiply. (x+3)(x+9)Ch. 6.2 - Use FOIL to multiply. (y+2)(y+5)Ch. 6.2 - Use FOIL to multiply. (a+6)(a+2)Ch. 6.2 - Use FOIL to multiply. (x+4)(x+1)Ch. 6.2 - Use FOIL to multiply. (y+4)(y8)Ch. 6.2 - Use FOIL to multiply. (a+7)(a4)Ch. 6.2 - Use FOIL to multiply. (x+2)(x4)Ch. 6.2 - Use FOIL to multiply. (x+3)(x5)Ch. 6.2 - Use FOIL to multiply. (x4)(x+2)Ch. 6.2 - Use FOIL to multiply. (m3)(m+5)Ch. 6.2 - Use FOIL to multiply. (2x+1)(x+2)Ch. 6.2 - Use FOIL to multiply. (3x+1)(x+2)Ch. 6.2 - Use FOIL to multiply. (3x3)(x1)Ch. 6.2 - Use FOIL to multiply. (4x3)(x1)Ch. 6.2 - Use FOIL to multiply. (2y1)(y+2)Ch. 6.2 - Use FOIL to multiply. (4y2)(y+1)Ch. 6.2 - Use FOIL to multiply. (2y+1)(y2)Ch. 6.2 - Use FOIL to multiply. (4y+2)(y1)Ch. 6.2 - Multiply. 5a(2a4b6)Ch. 6.2 - Multiply. 4x(3x+5y7)Ch. 6.2 - Multiply. 7x3(x3)Ch. 6.2 - Multiply. 8x3(x5)Ch. 6.2 - Prob. 51ECh. 6.2 - Multiply. (x4)(x2+x2)Ch. 6.2 - Multiply. (z+2)(z5)Ch. 6.2 - Multiply. (b+1)(b3)Ch. 6.2 - Multiply. (2x+1)(4x2+2x8)Ch. 6.2 - Multiply. (3x+1)(2x2+3x2)Ch. 6.2 - Multiply. (y7)(y+2)Ch. 6.2 - Multiply. (y8)(y+5)Ch. 6.2 - Prob. 59ECh. 6.2 - Multiply. a. (z+2)(z+4) b. (z2)(z4)Ch. 6.2 - Multiply. a. (x5)(x+3) b. (x+5)(x3)Ch. 6.2 - Prob. 62ECh. 6.2 - Simplify. (x+2)(x1)+2(3x+3)Ch. 6.2 - Simplify. (x3)(x+1)+4(2x+1)Ch. 6.2 - Simplify. 2x(x2+3x1)+(x2)(x3)Ch. 6.2 - Simplify. 3x(x2+x2)+(x1)(x2)Ch. 6.2 - If a(2x3)=14x+21, what is the value of a?Ch. 6.2 - If b(3xx+4)=15x20, what is the value of b?Ch. 6.2 - Perform the operations indicated. [3.2.3]Coin...Ch. 6.2 - Prob. 70ECh. 6.2 - Perform the operations indicated. [4.6.3]Calories...Ch. 6.2 - Perform the operations indicated. [4.5.3]Earnings...Ch. 6.2 - Prob. 1QQCh. 6.2 - Multiply. (x1)(4x22x+8)Ch. 6.2 - Prob. 3QQCh. 6.2 - Concept Check Multiply each of the following. 1....Ch. 6.3 - Fill in the blanks. Age Comparison Juan is two...Ch. 6.3 - Fill in the blanks. Age Comparison Rhonda is three...Ch. 6.3 - Fill in the blanks. Miles Run Alice can run 1 mile...Ch. 6.3 - Fill in the blanks. Home Runs Last season Jose...Ch. 6.3 - Prob. 5ECh. 6.3 - Write an applied problem using the following...Ch. 6.3 - Geometry The second angle of a triangle is 20...Ch. 6.3 - Wage Comparison Victors monthly salary is $95 less...Ch. 6.3 - Company Profit A companys profit for the fourth...Ch. 6.3 - Fundraiser Andrew walked 4 miles more than Dave...Ch. 6.3 - Height Comparison The height of a pole is one-half...Ch. 6.3 - Enrollment The number of students enrolled in Eden...Ch. 6.3 - Geometry The length of a rectangle is double the...Ch. 6.3 - Prob. 14ECh. 6.3 - Geometry The width of a rectangle is 13 inches...Ch. 6.3 - Geometry The width of a rectangle is 25 inches...Ch. 6.3 - Music DVDs The number of music DVDs that Carl has...Ch. 6.3 - Company Profit A companys profit for the second...Ch. 6.3 - Geometry The length of a rectangular box is double...Ch. 6.3 - Geometry The width of a rectangular box is double...Ch. 6.3 - Model Car Collection Jim has sixteen more blue...Ch. 6.3 - Height Comparison Sion is 3 inches taller than...Ch. 6.3 - Geometry The second side of a triangle is 4 inches...Ch. 6.3 - Geometry The second side of a triangle is 3 inches...Ch. 6.3 - Height Comparison The height of a building is four...Ch. 6.3 - Geometry The length of a yard is triple the length...Ch. 6.3 - School Election In a school election for class...Ch. 6.3 - Cookie Sales Betty-Jo sold 20 fewer boxes of Girl...Ch. 6.3 - Wage Comparison Vus salary is $125 more than Sams...Ch. 6.3 - Computer Game Scores Lena earned 120 points less...Ch. 6.3 - Investment Jerry invested $3000 more in stocks...Ch. 6.3 - Music Downloads The number of songs Arnold...Ch. 6.3 - Answer true or false. We can solve 3x+6.Ch. 6.3 - Answer true or false. We can solve 3x+6=12.Ch. 6.3 - Solve [3.2.1] 11x=44Ch. 6.3 - Solve [3.2.1] y+77=6Ch. 6.3 - Solve [5.7.1] m7=5Ch. 6.3 - Solve [3.1.2] 4x3x+8=62Ch. 6.3 - [3.3.2] Find the area of a rectangle with...Ch. 6.3 - [3.3.2] Find the volume of a rectangle with...Ch. 6.3 - Tinas monthly salary is triple Mais monthly...Ch. 6.3 - Dixie is 4 years older than Sugar. Pumpkin is 3...Ch. 6.3 - Phoebe purchased a watch, ring, and bracelet at...Ch. 6.3 - Concept Check The width of a box is triple the...Ch. 6.4 - Jessie incorrectly factored 6x12 as follows:...Ch. 6.4 - Explain why the following polynomial is not...Ch. 6.4 - For 9 and 27: a. State the common factors. b....Ch. 6.4 - For 4 and 24: a. State the common factors. b....Ch. 6.4 - Find the GCF for each set of numbers. 4, 16Ch. 6.4 - Find the GCF for each set of numbers. 5, 20Ch. 6.4 - Find the GCF for each set of numbers. 18, 27Ch. 6.4 - Find the GCF for each set of numbers. 14, 21Ch. 6.4 - Find the GCF for each set of numbers. 6, 9, 15Ch. 6.4 - Find the GCF for each set of numbers. 8, 10, 12Ch. 6.4 - Find the GCF for each set of numbers. 10, 15, 20Ch. 6.4 - Find the GCF for each set of numbers. 12, 18, 24Ch. 6.4 - For the polynomial a3bc+a6c: a. What variables are...Ch. 6.4 - For the polynomial x4yzx2z: a. What variables are...Ch. 6.4 - Find the GCF for each expression. xy2+xy3Ch. 6.4 - Find the GCF for each expression. mn3+mn4Ch. 6.4 - Find the GCF for each expression. a2b5+a3b4Ch. 6.4 - Find the GCF for each expression. x3y4+x2y5Ch. 6.4 - Find the GCF for each expression. a3bc2+ac3Ch. 6.4 - Find the GCF for each expression. x2yz3+xz2Ch. 6.4 - Find the GCF for each expression. x3yz3+xy4Ch. 6.4 - Find the GCF for each expression. a2bc3+ab3Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing numbers or variables needed to...Ch. 6.4 - Fill in the missing + or sign. a. b.Ch. 6.4 - Fill in the missing + or sign. a. b.Ch. 6.4 - Factor. Check by multiplying. 3a6Ch. 6.4 - Factor. Check by multiplying. 7x14Ch. 6.4 - Factor. Check by multiplying. 5y+5Ch. 6.4 - Factor. Check by multiplying. 9x+9Ch. 6.4 - Factor. Check by multiplying. 10a+4bCh. 6.4 - Factor. Check by multiplying. 6x+10yCh. 6.4 - Factor. Check by multiplying. 15m+3nCh. 6.4 - Factor. Check by multiplying. 5a+25bCh. 6.4 - Factor. Check by multiplying. 7x+14y+21Ch. 6.4 - Factor. Check by multiplying. 6a+42b+30Ch. 6.4 - Factor. Check by multiplying. 8a+18b6Ch. 6.4 - Factor. Check by multiplying. 15x+20y10Ch. 6.4 - Factor. Check by multiplying. 2a24aCh. 6.4 - Factor. Check by multiplying. 15y23yCh. 6.4 - Factor. Check by multiplying. 4abb2Ch. 6.4 - Factor. Check by multiplying. 5xyy2Ch. 6.4 - Factor. Check by multiplying. 5x+10xyCh. 6.4 - Factor. Check by multiplying. 9x+18xyCh. 6.4 - Factor. Check by multiplying. 7x2y14xyCh. 6.4 - Factor. Check by multiplying. 8a2b16abCh. 6.4 - Factor. Check by multiplying. 12a2b6a2Ch. 6.4 - Factor. Check by multiplying. 15ab35b3Ch. 6.4 - Factor. Check by multiplying. 3x29x+18Ch. 6.4 - Factor. Check by multiplying. 2x28x+12Ch. 6.4 - Factor and check your answer. 4x2+8x3Ch. 6.4 - Factor and check your answer. 3y3+9y2Ch. 6.4 - Factor and check your answer. 2x2y+4xyCh. 6.4 - Factor and check your answer. 3a2b+6abCh. 6.4 - Factor and check your answer. 4y+2Ch. 6.4 - Factor and check your answer. 10x+5Ch. 6.4 - Factor and check your answer. 15a20Ch. 6.4 - Factor and check your answer. 9b15Ch. 6.4 - Factor and check your answer. 5x10xyCh. 6.4 - Factor and check your answer. 9x18xyCh. 6.4 - Factor and check your answer. 9xy33xyCh. 6.4 - Factor and check your answer. 4xy22xyCh. 6.4 - Factor and check your answer. 6x3y+12Ch. 6.4 - Factor and check your answer. 10a+20b+25Ch. 6.4 - Factor and check your answer. 4x2+8x4Ch. 6.4 - Factor and check your answer. 9x2+18x9Ch. 6.4 - Factor and check your answer. 2x3y38x2y2Ch. 6.4 - Factor and check your answer. 5x3y310x2y2Ch. 6.4 - Factor and check your answer. 4a2b+6ab+8aCh. 6.4 - Factor and check your answer. 12xy2+4xy+8yCh. 6.4 - When factoring a polynomial whose first...Ch. 6.4 - When factoring a polynomial whose first...Ch. 6.4 - Find the least common denominator of each set of...Ch. 6.4 - Find the least common denominator of each set of...Ch. 6.4 - Find the least common denominator of each set of...Ch. 6.4 - Find the least common denominator of each set of...Ch. 6.4 - [5.6.1]Rainfall Measured A rain gauge collected...Ch. 6.4 - [4.6.4]Potato Salad Servings Louise ordered 45...Ch. 6.4 - Find the GCF. a. 12, 20, 36 b. x2yz2x2y2Ch. 6.4 - Factor. 4x210y+2Ch. 6.4 - Factor. 5ab215abCh. 6.4 - Concept Check For the expression 12xy+16x a. Is xy...Ch. 6 - Prob. 1RPCh. 6 - Identify the terms of each polynomial. a42b23b4Ch. 6 - Simplify.Ch. 6 - Simplify. (6x+4y2)Ch. 6 - Perform the operations indicated. (3x9)+(5x2)Ch. 6 - Perform the operations indicated. (4x+8)(8x+2)Ch. 6 - Perform the operations indicated....Ch. 6 - Perform the operations indicated....Ch. 6 - Perform the operations indicated....Ch. 6 - Perform the operations indicated....Ch. 6 - Multiply. 4(6x28x+5)Ch. 6 - Prob. 12RPCh. 6 - Multiply. 3x(9x3y+2)Ch. 6 - Multiply. 5n(4n9m7)Ch. 6 - Multiply. 4x2(x44)Ch. 6 - Multiply. x4(x52x3)Ch. 6 - Multiply. (z+4)(5z)Ch. 6 - Multiply. (y+10)(6y)Ch. 6 - Multiply. (x36x)(4x2)Ch. 6 - Multiply. (x2)(2x2+3x1)Ch. 6 - Prob. 21RPCh. 6 - Multiply. (y1)(3y2+4y+5)Ch. 6 - Multiply. (2x+3)(x2+3x1)Ch. 6 - Use the FOIL method to multiply. (x2)(x+4)Ch. 6 - Use the FOIL method to multiply. (y+4)(y7)Ch. 6 - Use the FOIL method to multiply. (x2)(3x+4)Ch. 6 - Use the FOIL method to multiply. (x3)(5x6)Ch. 6 - Company Profit A companys profit for the third...Ch. 6 - Geometry The width of a field is 22 feet shorter...Ch. 6 - Geometry The measure of a is 30 more than the...Ch. 6 - Floral Bouquet A floral shop puts three times as...Ch. 6 - Wage Comparison Phoebes salary is $145 more than...Ch. 6 - Eye Color In a first-period history class at a...Ch. 6 - Geometry The length of the second side of a...Ch. 6 - Geometry The length of a box is 7 inches longer...Ch. 6 - Find the GCF for each of the following. 14, 21Ch. 6 - Find the GCF for each of the following. 6, 21Ch. 6 - Find the GCF for each of the following. 25, 45Ch. 6 - Find the GCF for each of the following. 18, 36Ch. 6 - Find the GCF for each of the following. 8, 14, 18Ch. 6 - Find the GCF for each of the following. 12, 16, 20Ch. 6 - Find the GCF for each of the following. a2bc+ab3Ch. 6 - Find the GCF for each of the following. xy3z+x2y2Ch. 6 - Factor. 6x14Ch. 6 - Factor. 5x+15Ch. 6 - Factor. 4a+12bCh. 6 - Factor. 3y9zCh. 6 - Factor. 6xy212xyCh. 6 - Factor. 8a2b16abCh. 6 - Factor. 10x3y+5x2yCh. 6 - Factor. 4y36y2+2yCh. 6 - Factor. 3a6b+12Ch. 6 - Factor. 2x+4y10Ch. 6 - Write the answers. Identify the terms of the...Ch. 6 - Write the answers. Simplify. (4x2y6)Ch. 6 - Perform the operations indicated. (5x+3)+(2x+4)Ch. 6 - Perform the operations indicated. (4y+5)(2y3)Ch. 6 - Perform the operations indicated. (7p2)(3p+4)Ch. 6 - Perform the operations indicated....Ch. 6 - Perform the operations indicated....Ch. 6 - Perform the operations indicated....Ch. 6 - Prob. 9TCh. 6 - Multiply. 7a(2a+3b4)Ch. 6 - Multiply. 2x3(4x23)Ch. 6 - Multiply. (x+5)(x+9)Ch. 6 - Multiply. (x+3)(x2)Ch. 6 - Multiply. (2x+1)(x3)Ch. 6 - Multiply. (3x31)(4x4)Ch. 6 - Prob. 16TCh. 6 - The width of a piece of wood is three inches...Ch. 6 - The second side of a triangle is 6 inches longer...Ch. 6 - Jason received 3000 fewer votes than Lena in an...Ch. 6 - Find the GCF. 9, 21Ch. 6 - Find the GCF. 8, 16, 20Ch. 6 - Find the GCF. x2yz+x3zCh. 6 - Factor. 3x+12Ch. 6 - Factor. 7x214x+21Ch. 6 - Factor. 2x2y6xy2
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