problem solving combine like terms lesson 7.7 answer key

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Convert Units of Length - Lesson 6.1

Convert Units of Capacity - Lesson 6.2

Convert Units of Weight and Mass - Lesson 6.3

Transform Units - Lesson 6.4

Problem Solving - Distance, Rate, and Time - Lesson 6.5

Fractions and Decimals - Lesson 2.1

Compare and order Fractions and Decimals - Lesson 2.2

Multiply Fractions - Lesson 2.3

Simplify Factors - Lesson 2.4

Model Fraction Division - Lesson 2.5

Estimate Quotients - Lesson 2.6

Dividing Fractions - Lesson 2.7

Model Mixed Number Division - Lesson 2.8

Divide Mixed Numbers - Lesson 2.9

Problem Solving - Fraction Operations - Lesson 2.10

Understanding Positive and Negative Integers - Lesson 3.1

Compare and Order Integers - Lesson 3.2

Rational Numbers and the Number Line - Lesson 3.3

Compare and Order Rational Numbers - Lesson 3.4

Absolute Value - Lesson 3.5

Compare Absolute Value - Lesson 3.6

Rational Numbers and the Coordinate Plane - Lesson 3.7

Ordered Pair Relationships - Lesson 3.8

Distance on the Coordinate Plane - Lesson 3.9

Problem Solving - The Coordinate Plane - Lesson 3.10

Solutions of Equations - Lesson 8.1

Writing Equations - Lesson 8.2

Model and Solve Addition Equations - Lesson 8.3

Solve Addition & Subtraction Equations - Lesson 8.4

Sixth Grade

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Model Ratios - Lesson 4.1

Ratios and Rates - Lesson 4.2

Equivalent Ratios and the Multiplication Table - Lesson 4.3

Use Tables to Compare Ratios - Lesson 4.4

Use Equivalent Ratios - Lesson 4.5

Find Unit Rates - Lesson 4.6

Use Unit Rates - Lesson 4.7

Equivalent Ratios and Graphs - Lesson 4.8

Three Dimensional Figures and Nets - Lesson 11.1

Surface Area of Prisms - Lesson 11.3

Surface Area of Pyramids - Lesson 11.4

Volume of a Rectangular Prism - Lesson 11.6

Area of Parallelograms - Lesson 10.1

Explore Area of Triangles - Lesson 10.2

Area of Triangles - Lesson 10.3

Explore Area of Trapezoids - Lesson 10.4

Area of Trapezoids - Lesson 10.5

Area of Regular Polygons - Lesson 10.6

​Composite Figures - Lesson 10.7

Divide Multi-Digit Numbers - Lesson 1.1

Prime Factorization - Lesson 1.2

Least Common Multiple (LCM) - Lesson 1.3

Greatest Common Factor (GCF) - Lesson 1.4

Problem Solving: Apply the GCF - Lesson 1.5

Add and Subtract Decimals - Lesson 1.6

Multiply Decimals - Lesson 1.7

Divide Decimals by Whole Numbers - Lesson 1.8

Divide with Decimals - Lesson 1.9

Chapter 1 Review for Test

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Exponents - Lesson 7.1

Evaluating Expressions Involving Exponents - Lesson 7.2

Write Algebraic Expressions - Lesson 7.3

Identify Parts of Expressions - Lesson 7.4

Evaluate Algebraic Expressions and Formulas - Lesson 7.5

Use Algebraic Expressions - Lesson 7.6

Problem Solving - Combining Like Terms - Lesson 7.7

Generate Equivalent Expressions - Lesson 7.8

Identify Equivalent Expressions - Lesson 7.9

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Independent and Dependent Variables - Lesson 9.1

Equations and Tables - Lesson 9.2

Model Percents - Lesson 5.1

Write Percents as Fractions and Decimals - Lesson 5.2

Write Fractions and Decimals as Percents - Lesson 5.3

Percent of a Quantity - Lesson 5.4

Problem Solving - Percents - Lesson 5.5

Find the Whole From a Percent - Lesson 5.6

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Go Math 6th Grade Lesson 7.7

Mathematics.

4 questions

Introducing new   Paper mode

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A box of pens cost $3 and a box of markers costs $5. The expression 3p+5p represents the cost in dollars to make p packages that include 1 box of pens and 1 box of markers. simplify the expression by combing like terms.

Riley's parents got a cell phone plan that has a $40 monthly fee for the first phone. For each extra phone, there is a $15 phone service charge and $10 text service charge. THe expression 40+15e represents the total phone bill in dollars, where e is the number of extra phones. Simplify the expression if possible by combining like terms.

A radio show last for h hours. For every 60 minutes of air time during the show, there are 8 minutes of commercials. The expression 60h-8h represents the air time in minutes available for talk and music. Simplify the expression by combining like terms.

A sub shop sells a meal that includes an Italian sub for $6 and chips for $2 . If a customer purchases more than 3 meals, he or she receives a $5 discount. The expression for 6m+2m-5 shows the cost in dollars of the customer's order for m meals, where m is greater than 3. Simplify the expression by combining like terms.

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Answer Key 7.7

• [latex]6a(4c-3b)+15d(4c-3b)[/latex] [latex](4c-3b)(6a+15d)[/latex] [latex]3(4c-3b)(2a+5d)[/latex]
• [latex]-6\times -5=30[/latex] [latex]-6+-5=-11[/latex] [latex]2x^2-6x-5x+15[/latex] [latex]2x(x-3)-5(x-3)[/latex] [latex](x-3)(2x-5)[/latex]
• [latex]-5\times -4=20[/latex] [latex]-5+-4=-9[/latex] [latex]5u^2-5uv-4uv+4v^2[/latex] [latex]5u(u-v)-4v(u-v)[/latex] [latex](u-v)(5u-4v)[/latex]
• [latex](4x+6y)^2[/latex]
• [latex]-2(x^3-64y^3)[/latex] [latex]-2(x-4y)(x^2+4xy+16y^2)[/latex]
• [latex]20u(v-3u^2)-5x(v-3u^2)[/latex] [latex](v-3u^2)(20u-5x)[/latex]
• [latex]2(27u^3-8)[/latex] [latex]2(3u-2)(9u^2+6u+4)[/latex]
• [latex]2(27-64x^3)[/latex] [latex]2(3-4x)(9+12x+16x^2)[/latex]
• [latex]n(n-1)[/latex]
• [latex]-25\times 3=-75[/latex] [latex]-25+3=-22[/latex] [latex]5x^2-25x+3x-15[/latex] [latex]5x(x-5)+3(x-5)[/latex] [latex](x-5)(5x+3)[/latex]
• [latex]x^2-3xy-xy+3y^2[/latex] [latex]x(x-3y)-y(x-3y)[/latex] [latex](x-3y)(x-y)[/latex]
• [latex]-15\times -15=225[/latex] [latex]-15+-15=-30[/latex] [latex]5(9u^2-30uv+25v^2)[/latex] [latex]5(9u^2-15uv-15uv+25v^2)[/latex] [latex]5(3u(3u-5v)-5v(3u-5v))[/latex] [latex]5(3u-5v)(3u-5v)[/latex]
• [latex](m-2n)(m+2n)[/latex]
• [latex]3(4ab-6a+2nb-3n)[/latex] [latex]3(2a(2b-3)+n(2b-3))[/latex] [latex]3(2b-3)(2a+n)[/latex]
• [latex]36b^2c-24b^2d+24ac-16ad[/latex] [latex]12b^2(3c-2d)+8a(3c-2d)[/latex] [latex](3c-2d)(12b^2+8a)[/latex] [latex]4(3c-2d)(3b^2+2a)[/latex]
• [latex]-4\times 2=-8[/latex] [latex]-4+2=-2[/latex] [latex]3m(m^2-2mn-8n^2)[/latex] [latex]3m(m^2-4mn+2mn-8n^2)[/latex] [latex]3m(m(m-4n)+2n(m-4n))[/latex] [latex]3m(m-4n)(m+2n)[/latex]
• [latex]2(64+27x^3)[/latex] [latex]2(4+3x)(16-12x+9x^2)[/latex]
• [latex](4m+3n)(16m^2-12mn+9n^2)[/latex]
• [latex]5\times 2=10[/latex] [latex]5+2=7[/latex] [latex]n(n^2+7n+10)[/latex] [latex]n(n^2+5n+2n+10)[/latex] [latex]n(n(n+5)+2(n+5))[/latex] [latex]n(n+5)(n+2)[/latex]
• [latex](4m-n)(16m^2+4mn+n^2)[/latex]
• [latex](3x-4)(9x^2+12x+16)[/latex]
• [latex](4a-3b)(4a+3b)[/latex]
• [latex]x(5x+2)[/latex]
• [latex]-6\times -4=24[/latex] [latex]-6+-4=-10[/latex] [latex]2x^2-6x-4x+12[/latex] [latex]2x(x-3)-4(x-3)[/latex] [latex](x-3)(2x-4)[/latex]

Intermediate Algebra Copyright © 2020 by Terrance Berg is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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ⓐ x = 0 x = 0 ⓑ n = − 1 3 n = − 1 3 ⓒ a = −1 , a = −3 a = −1 , a = −3

ⓐ q = 0 q = 0 ⓑ y = − 2 3 y = − 2 3 ⓒ m = 2 , m = −3 m = 2 , m = −3

x + 1 x − 1 , x + 1 x − 1 , x ≠ 2 , x ≠ 2 , x ≠ 1 x ≠ 1

x − 5 x − 1 , x − 5 x − 1 , x ≠ − 2 , x ≠ − 2 , x ≠ 1 x ≠ 1

2 ( x − 3 y ) 3 ( x + 3 y ) 2 ( x − 3 y ) 3 ( x + 3 y )

5 ( x − y ) 2 ( x + 5 y ) 5 ( x − y ) 2 ( x + 5 y )

− x + 1 x + 5 − x + 1 x + 5

− x + 2 x + 1 − x + 2 x + 1

x − 2 2 ( x + 3 ) x − 2 2 ( x + 3 )

3 ( x − 6 ) x + 5 3 ( x − 6 ) x + 5

x − 4 x − 5 x − 4 x − 5

− ( b + 2 ) ( b − 1 ) ( 1 + b ) ( b + 4 ) − ( b + 2 ) ( b − 1 ) ( 1 + b ) ( b + 4 )

2 ( x 2 + 2 x + 4 ) ( x + 2 ) ( x 2 − 2 x + 4 ) 2 ( x 2 + 2 x + 4 ) ( x + 2 ) ( x 2 − 2 x + 4 )

2 z z − 1 2 z z − 1

x + 2 4 x + 2 4

2 y + 5 2 y + 5

2 ( m + 1 ) ( m + 2 ) 3 ( m + 4 ) ( m − 3 ) 2 ( m + 1 ) ( m + 2 ) 3 ( m + 4 ) ( m − 3 )

( n + 5 ) ( n + 9 ) 2 ( n + 6 ) ( 2 n + 3 ) ( n + 5 ) ( n + 9 ) 2 ( n + 6 ) ( 2 n + 3 )

The domain of R ( x ) R ( x ) is all real numbers where x ≠ 5 x ≠ 5 and x ≠ − 1 . x ≠ − 1 .

The domain of R ( x ) R ( x ) is all real numbers where x ≠ 4 x ≠ 4 and x ≠ − 2 . x ≠ − 2 .

R ( x ) = 2 R ( x ) = 2

R ( x ) = 1 3 R ( x ) = 1 3

R ( x ) = x − 2 4 ( x − 8 ) R ( x ) = x − 2 4 ( x − 8 )

R ( x ) = x ( x − 2 ) x − 1 R ( x ) = x ( x − 2 ) x − 1

x + 2 x + 2

x + 3 x + 3

x − 11 x − 2 x − 11 x − 2

x − 3 x + 9 x − 3 x + 9

y + 3 y + 2 y + 3 y + 2

3 n − 2 n − 1 3 n − 2 n − 1

ⓐ ( x − 4 ) ( x + 3 ) ( x + 4 ) ( x − 4 ) ( x + 3 ) ( x + 4 ) ⓑ 2 x + 8 ( x − 4 ) ( x + 3 ) ( x + 4 ) 2 x + 8 ( x − 4 ) ( x + 3 ) ( x + 4 ) , x + 3 ( x − 4 ) ( x + 3 ) ( x + 4 ) x + 3 ( x − 4 ) ( x + 3 ) ( x + 4 )

ⓐ ( x + 2 ) ( x − 5 ) ( x + 1 ) ( x + 2 ) ( x − 5 ) ( x + 1 ) ⓑ 3 x 2 + 3 x ( x + 2 ) ( x − 5 ) ( x + 1 ) 3 x 2 + 3 x ( x + 2 ) ( x − 5 ) ( x + 1 ) , 5 x − 25 ( x + 2 ) ( x − 5 ) ( x + 1 ) 5 x − 25 ( x + 2 ) ( x − 5 ) ( x + 1 )

7 x − 4 ( x − 2 ) ( x + 3 ) 7 x − 4 ( x − 2 ) ( x + 3 )

7 m + 25 ( m + 3 ) ( m + 4 ) 7 m + 25 ( m + 3 ) ( m + 4 )

5 m 2 − 9 m + 2 ( m + 1 ) ( m − 2 ) ( m + 2 ) 5 m 2 − 9 m + 2 ( m + 1 ) ( m − 2 ) ( m + 2 )

2 n 2 + 12 n − 30 ( n + 2 ) ( n − 5 ) ( n + 3 ) 2 n 2 + 12 n − 30 ( n + 2 ) ( n − 5 ) ( n + 3 )

1 x − 2 1 x − 2

−3 z − 3 −3 z − 3

5 x + 1 ( x − 6 ) ( x + 1 ) 5 x + 1 ( x − 6 ) ( x + 1 )

y + 3 y + 4 y + 3 y + 4

1 ( b + 1 ) ( b − 1 ) 1 ( b + 1 ) ( b − 1 )

1 ( x + 2 ) ( x + 1 ) 1 ( x + 2 ) ( x + 1 )

v + 3 v + 1 v + 3 v + 1

3 w w + 7 3 w w + 7

x − 7 x − 4 x − 7 x − 4

x 2 − 3 x + 18 ( x + 3 ) ( x − 3 ) x 2 − 3 x + 18 ( x + 3 ) ( x − 3 )

2 3 ( x − 1 ) 2 3 ( x − 1 )

1 2 ( x − 3 ) 1 2 ( x − 3 )

14 11 14 11

10 23 10 23

y + x y − x y + x y − x

a b b − a a b b − a

b ( b + 2 ) ( b − 5 ) 3 b − 5 b ( b + 2 ) ( b − 5 ) 3 b − 5

3 c + 3 3 c + 3

b + a a 2 + b 2 b + a a 2 + b 2

y − x x y y − x x y

3 ( x − 2 ) 5 x + 7 3 ( x − 2 ) 5 x + 7

x + 21 6 x − 43 x + 21 6 x − 43

3 5 x + 22 3 5 x + 22

2 ( 2 y 2 + 13 y + 5 ) 3 y 2 ( 2 y 2 + 13 y + 5 ) 3 y

x x + 4 x x + 4

x ( x + 1 ) 3 ( x − 1 ) x ( x + 1 ) 3 ( x − 1 )

y = − 7 15 y = − 7 15

x = 13 15 x = 13 15

x = −3 , x = 5 x = −3 , x = 5

y = −2 , y = 6 y = −2 , y = 6

x = 2 3 x = 2 3

y = 2 y = 2

There is no solution.

x = 3 x = 3

y = 7 y = 7

ⓐ The domain is all real numbers except x ≠ 3 x ≠ 3 and x ≠ 4 . x ≠ 4 . ⓑ x = 2 , x = 14 3 x = 2 , x = 14 3 ⓒ ( 2 , 3 ) , ( 14 3 , 3 ) ( 2 , 3 ) , ( 14 3 , 3 )

ⓐ The domain is all real numbers except x ≠ 1 x ≠ 1 and x ≠ 5 . x ≠ 5 . ⓑ x = 21 4 x = 21 4 ⓒ ( 21 4 , 4 ) ( 21 4 , 4 )

y = m x − 4 m + 5 y = m x − 4 m + 5

y = m x + 5 m + 1 y = m x + 5 m + 1

a = b c b − 1 a = b c b − 1

y = 3 x x + 6 y = 3 x x + 6

y = 33 y = 33

z = 14 z = 14

The pediatrician will prescribe 12 ml of acetaminophen to Emilia.

The pediatrician will prescribe 180 mg of fever reducer to Isabella.

The distance is 150 miles.

The distance is 350 miles.

The telephone pole is 40 feet tall.

The pine tree is 60 feet tall.

Link’s biking speed is 15 mph.

The speed of Danica’s boat is 17 mph.

Dennis’s uphill speed was 10 mph and his downhill speed was 5 mph.

Joon’s rate on the country roads is 50 mph.

Kayla’s biking speed was 15 mph.

Victoria jogged 6 mph on the flat trail.

When the two gardeners work together it takes 2 hours and 24 minutes.

When Daria and her mother work together it takes 2 hours and 6 minutes.

Kristina can paint the room in 12 hours.

It will take Jordan 6 hours.

ⓐ c = 4.8 t c = 4.8 t ⓑ He would burn 432 calories.

ⓐ d = 50 t d = 50 t ⓑ It would travel 250 miles.

ⓐ h = 130 t h = 130 t ⓑ 1 2 3 1 2 3 hours

ⓐ x = 3500 p x = 3500 p ⓑ 500 units

( − ∞ , −4 ) ∪ [ 2 , ∞ ) ( − ∞ , −4 ) ∪ [ 2 , ∞ )

( − ∞ , −2 ] ∪ ( 4 , ∞ ) ( − ∞ , −2 ] ∪ ( 4 , ∞ )

( − 3 2 , 3 ) ( − 3 2 , 3 )

( −8 , 4 ) ( −8 , 4 )

( − ∞ , −4 ) ∪ ( 2 , ∞ ) ( − ∞ , −4 ) ∪ ( 2 , ∞ )

( − ∞ , −4 ) ∪ ( 3 , ∞ ) ( − ∞ , −4 ) ∪ ( 3 , ∞ )

( 2 , 4 ) ( 2 , 4 )

( 3 , 6 ) ( 3 , 6 )

( −4 , 2 ] ( −4 , 2 ]

[ −1 , 4 ) [ −1 , 4 )

ⓐ c ( x ) = 20 x + 6000 x c ( x ) = 20 x + 6000 x ⓑ More than 150 items must be produced to keep the average cost below $60 per item.

ⓐ c ( x ) = 5 x + 900 x c ( x ) = 5 x + 900 x ⓑ More than 60 items must be produced to keep the average cost below $20 per item.

Section 7.1 Exercises

ⓐ z = 0 z = 0 ⓑ p = 5 6 p = 5 6 ⓒ n = −4 , n = 2 n = −4 , n = 2

ⓐ y = 0 y = 0 , ⓑ x = − 1 2 x = − 1 2 , ⓒ u = −4 , u = 7 u = −4 , u = 7

− 4 5 − 4 5

2 m 2 3 n 2 m 2 3 n

x + 5 x − 1 x + 5 x − 1

a + 2 a + 8 a + 2 a + 8

p 2 + 4 p − 2 p 2 + 4 p − 2

4 b ( b − 4 ) ( b + 5 ) ( b − 8 ) 4 b ( b − 4 ) ( b + 5 ) ( b − 8 )

3 ( m + 5 n ) 4 ( m − 5 n ) 3 ( m + 5 n ) 4 ( m − 5 n )

− 5 y + 4 − 5 y + 4

w 2 − 6 w + 36 w − 6 w 2 − 6 w + 36 w − 6

− z − 5 4 + z − z − 5 4 + z

x 3 8 y x 3 8 y

p ( p − 4 ) 2 ( p − 9 ) p ( p − 4 ) 2 ( p − 9 )

y − 5 3 ( y + 5 ) y − 5 3 ( y + 5 )

− 4 ( b + 9 ) 3 ( b + 7 ) − 4 ( b + 9 ) 3 ( b + 7 )

c + 5 3 c + 1 c + 5 3 c + 1

( m − 3 ) ( m − 2 ) ( m + 4 ) ( m + 3 ) ( m − 3 ) ( m − 2 ) ( m + 4 ) ( m + 3 )

− 1 v + 5 − 1 v + 5

3 s s + 4 3 s s + 4

4 ( p 2 − p q + q 2 ) ( p − q ) ( p 2 + p q + q 2 ) 4 ( p 2 − p q + q 2 ) ( p − q ) ( p 2 + p q + q 2 )

x − 2 8 x ( x + 5 ) x − 2 8 x ( x + 5 )

2 a − 7 5 2 a − 7 5

3 ( 3 c − 5 ) 3 ( 3 c − 5 )

4 ( m + 8 ) ( m + 7 ) 3 ( m − 4 ) ( m + 2 ) 4 ( m + 8 ) ( m + 7 ) 3 ( m − 4 ) ( m + 2 )

( 4 p + 1 ) ( p − 4 ) 3 p ( p + 9 ) ( p − 1 ) ( 4 p + 1 ) ( p − 4 ) 3 p ( p + 9 ) ( p − 1 )

x ≠ 5 x ≠ 5 and x ≠ − 5 x ≠ − 5

x ≠ 2 x ≠ 2 and x ≠ − 3 x ≠ − 3

R ( x ) = x + 5 2 x ( x + 2 ) R ( x ) = x + 5 2 x ( x + 2 )

R ( x ) = 3 x ( x + 7 ) x − 7 R ( x ) = 3 x ( x + 7 ) x − 7

R ( x ) = x ( x − 5 ) x − 6 R ( x ) = x ( x − 5 ) x − 6

Answers will vary.

Section 7.2 Exercises

3 c + 5 4 c − 5 3 c + 5 4 c − 5

r + 8 r + 8

2 w w − 4 2 w w − 4

3 a + 7 3 a + 7

m − 2 2 m − 2 2

p + 3 p + 5 p + 3 p + 5

r + 9 r + 7 r + 9 r + 7

z + 4 z − 5 z + 4 z − 5

4 b − 3 b − 7 4 b − 3 b − 7

ⓐ ( x + 2 ) ( x − 4 ) ( x + 3 ) ( x + 2 ) ( x − 4 ) ( x + 3 ) ⓑ 5 x + 15 ( x + 2 ) ( x − 4 ) ( x + 3 ) 5 x + 15 ( x + 2 ) ( x − 4 ) ( x + 3 ) , 2 x 2 + 4 x ( x + 2 ) ( x − 4 ) ( x + 3 ) 2 x 2 + 4 x ( x + 2 ) ( x − 4 ) ( x + 3 )

ⓐ ( z − 2 ) ( z + 4 ) ( z − 4 ) ( z − 2 ) ( z + 4 ) ( z − 4 ) ⓑ 9 z − 36 ( z − 2 ) ( z + 4 ) ( z − 4 ) 9 z − 36 ( z − 2 ) ( z + 4 ) ( z − 4 ) , 4 z 2 − 8 z ( z − 2 ) ( z + 4 ) ( z − 4 ) 4 z 2 − 8 z ( z − 2 ) ( z + 4 ) ( z − 4 )

ⓐ ( b + 3 ) ( b + 3 ) ( b − 5 ) ( b + 3 ) ( b + 3 ) ( b − 5 ) ⓑ 4 b − 20 ( b + 3 ) ( b + 3 ) ( b − 5 ) 4 b − 20 ( b + 3 ) ( b + 3 ) ( b − 5 ) , 2 b 2 + 6 b ( b + 3 ) ( b + 3 ) ( b − 5 ) 2 b 2 + 6 b ( b + 3 ) ( b + 3 ) ( b − 5 )

ⓐ ( d + 5 ) ( 3 d − 1 ) ( d − 6 ) ( d + 5 ) ( 3 d − 1 ) ( d − 6 ) ⓑ 2 d − 12 ( d + 5 ) ( 3 d − 1 ) ( d − 6 ) 2 d − 12 ( d + 5 ) ( 3 d − 1 ) ( d − 6 ) , 5 d 2 + 25 d ( d + 5 ) ( 3 d − 1 ) ( d − 6 ) 5 d 2 + 25 d ( d + 5 ) ( 3 d − 1 ) ( d − 6 )

21 y + 8 x 30 x 2 y 2 21 y + 8 x 30 x 2 y 2

5 r − 7 ( r + 4 ) ( r − 5 ) 5 r − 7 ( r + 4 ) ( r − 5 )

11 w + 1 ( 3 w − 2 ) ( w + 1 ) 11 w + 1 ( 3 w − 2 ) ( w + 1 )

2 y 2 + y + 9 ( y + 3 ) ( y − 1 ) 2 y 2 + y + 9 ( y + 3 ) ( y − 1 )

b ( 5 b + 10 + 2 a 2 ) a 2 ( b − 2 ) ( b + 2 ) b ( 5 b + 10 + 2 a 2 ) a 2 ( b − 2 ) ( b + 2 )

− m m + 4 − m m + 4

3 ( r 2 + 6 r + 18 ) ( r + 1 ) ( r + 6 ) ( r + 3 ) 3 ( r 2 + 6 r + 18 ) ( r + 1 ) ( r + 6 ) ( r + 3 )

2 ( 7 t − 6 ) ( t − 6 ) ( t + 6 ) 2 ( 7 t − 6 ) ( t − 6 ) ( t + 6 )

4 a 2 + 25 a − 6 ( a + 3 ) ( a + 6 ) 4 a 2 + 25 a − 6 ( a + 3 ) ( a + 6 )

−6 m − 6 −6 m − 6

p + 2 p + 3 p + 2 p + 3

3 r − 2 3 r − 2

4 ( 8 x + 1 ) 10 x − 1 4 ( 8 x + 1 ) 10 x − 1

x − 5 ( x − 4 ) ( x + 1 ) ( x − 1 ) x − 5 ( x − 4 ) ( x + 1 ) ( x − 1 )

1 ( x − 1 ) ( x + 1 ) 1 ( x − 1 ) ( x + 1 )

5 a 2 + 7 a − 36 a ( a − 2 ) 5 a 2 + 7 a − 36 a ( a − 2 )

c − 5 c + 2 c − 5 c + 2

3 ( d + 1 ) d + 2 3 ( d + 1 ) d + 2

ⓐ R ( x ) = − ( x + 8 ) ( x + 1 ) ( x − 2 ) ( x + 3 ) R ( x ) = − ( x + 8 ) ( x + 1 ) ( x − 2 ) ( x + 3 ) ⓑ R ( x ) = x + 1 x + 3 R ( x ) = x + 1 x + 3

ⓐ 3 ( 3 x + 8 ) ( x − 8 ) ( x + 8 ) 3 ( 3 x + 8 ) ( x − 8 ) ( x + 8 ) ⓑ R ( x ) = 3 x + 8 R ( x ) = 3 x + 8

ⓐ Answers will vary. ⓑ Answers will vary. ⓒ Answers will vary. ⓓ x + y x y x + y x y

Section 7.3 Exercises

a − 4 2 a a − 4 2 a

1 2 ( c − 2 ) 1 2 ( c − 2 )

12 13 12 13

20 57 20 57

n 2 + m m − n 2 n 2 + m m − n 2

r t t − r r t t − r

( x + 1 ) ( x − 3 ) 2 ( x + 1 ) ( x − 3 ) 2

4 a + 1 4 a + 1

c 2 + c c − d 2 c 2 + c c − d 2

p q q − p p q q − p

2 x − 10 3 x + 16 2 x − 10 3 x + 16

3 z − 19 3 z + 8 3 z − 19 3 z + 8

4 3 a − 7 4 3 a − 7

2 c + 29 5 c 2 c + 29 5 c

2 p − 5 5 2 p − 5 5

m ( m − 5 ) ( 4 m − 19 ) ( m + 5 ) m ( m − 5 ) ( 4 m − 19 ) ( m + 5 )

13 24 13 24

2 ( a − 4 ) 2 ( a − 4 )

3 m n n − m 3 m n n − m

( x − 1 ) ( x − 2 ) 6 ( x − 1 ) ( x − 2 ) 6

Section 7.4 Exercises

a = 10 a = 10

v = 40 21 v = 40 21

m = −2 , m = 4 m = −2 , m = 4

p = −5 , p = −4 p = −5 , p = −4

v = 14 v = 14

x = − 4 5 x = − 4 5

z = −145 z = −145

q = −18 , q = −1 q = −18 , q = −1

no solution no solution

b = −8 b = −8

d = 2 d = 2

m = 1 m = 1

s = 5 4 s = 5 4

x = − 4 3 x = − 4 3

no solution

> ⓐ The domain is all real numbers except x ≠ − 2 x ≠ − 2 and x ≠ − 4 . x ≠ − 4 . ⓑ x = −3 , x = − 14 5 x = −3 , x = − 14 5 ⓒ ( −3 , 5 ) , ( − 14 5 , 5 ) ( −3 , 5 ) , ( − 14 5 , 5 )

ⓐ The domain is all real numbers except x ≠ 2 x ≠ 2 and x ≠ 5 . x ≠ 5 . ⓑ x = 9 2 , x = 9 2 , ⓒ ( 9 2 , 2 ) ( 9 2 , 2 )

r = C 2 π r = C 2 π

w = 2 v + 7 w = 2 v + 7

c = b + 3 + 2 a a c = b + 3 + 2 a a

p = q 4 q − 2 p = q 4 q − 2

w = 15 v 10 + v w = 15 v 10 + v

n = 5 m + 23 4 n = 5 m + 23 4

c = E m 2 c = E m 2

y = 20 x 12 − x y = 20 x 12 − x

Section 7.5 Exercises

x = 49 x = 49

p = −11 p = −11

a = 16 a = 16

m = 60 m = 60

p = 30 p = 30

ⓐ 162 beats per minute ⓑ yes

159 159 calories

325 325 Canadian dollars

ⓐ 6 ⓑ 12 12

2 3 2 3 foot ( 8 8 in.)

247.3 247.3 feet

160 160 mph

650 650 mph

2 2 hours and 44 44 minutes

7 7 hours and 30 30 minutes

y = 14 3 x y = 14 3 x

p = 3.2 q p = 3.2 q

ⓐ P = 2.5 g P = 2.5 g ⓑ $ 82.50 $ 82.50

ⓐ m = 8 v m = 8 v ⓑ 16 16 liters

ⓐ L = 3 d 2 L = 3 d 2 ⓑ 300 300 pounds

y = 20 x y = 20 x

v = 3 w v = 3 w

ⓐ g = 92,400 w g = 92,400 w ⓑ 16.8 mpg

ⓐ t = 1000 r t = 1000 r ⓑ 2.5 2.5 hours

ⓐ c = 2 t c = 2 t ⓑ 1 1 cavity

ⓐ c = 2.5 m c = 2.5 m ⓑ $55

Section 7.6 Exercises

( − ∞ , −4 ) ∪ [ 3 , ∞ ) ( − ∞ , −4 ) ∪ [ 3 , ∞ )

[ −1 , 3 ) [ −1 , 3 )

( − ∞ , 1 ) ∪ ( 7 , ∞ ) ( − ∞ , 1 ) ∪ ( 7 , ∞ )

( −5 , 6 ) ( −5 , 6 )

( − 5 2 , 5 ) ( − 5 2 , 5 )

( − ∞ , −3 ) ∪ ( 6 , ∞ ) ( − ∞ , −3 ) ∪ ( 6 , ∞ )

[ −9 , 6 ) [ −9 , 6 )

( − ∞ , −6 ] ∪ ( 4 , ∞ ) ( − ∞ , −6 ] ∪ ( 4 , ∞ )

( − ∞ , −4 ) ∪ ( −3 , ∞ ) ( − ∞ , −4 ) ∪ ( −3 , ∞ )

( 1 , 4 ) ( 1 , 4 )

( − ∞ , −3 ) ∪ ( 5 2 , ∞ ) ( − ∞ , −3 ) ∪ ( 5 2 , ∞ )

( − ∞ , 2 3 ) ∪ ( 3 2 , ∞ ) ( − ∞ , 2 3 ) ∪ ( 3 2 , ∞ )

( − ∞ , 0 ) ∪ ( 0 , 4 ) ∪ ( 6 , ∞ ) ( − ∞ , 0 ) ∪ ( 0 , 4 ) ∪ ( 6 , ∞ )

[ −2 , 0 ) ∪ ( 0 , 4 ] [ −2 , 0 ) ∪ ( 0 , 4 ]

( −4 , 4 ) ( −4 , 4 )

[ −10 , −1 ) ∪ ( 2 , ∞ ) [ −10 , −1 ) ∪ ( 2 , ∞ )

( 2 , 5 ] ( 2 , 5 ]

( − ∞ , −2 ) ∪ [ 6 , ∞ ) ( − ∞ , −2 ) ∪ [ 6 , ∞ )

Review Exercises

a ≠ 2 3 a ≠ 2 3

y ≠ 0 y ≠ 0

x + 3 x + 4 x + 3 x + 4

−3 x 2 −3 x 2

3 x ( x + 6 ) ( x + 6 ) 3 x ( x + 6 ) ( x + 6 )

1 11 + w 1 11 + w

5 c + 4 5 c + 4

R ( x ) = 3 R ( x ) = 3

y + 5 y + 5

x + 4 x + 4

q − 3 q + 5 q − 3 q + 5

15 w + 2 6 w − 1 15 w + 2 6 w − 1

3 b − 2 b + 7 3 b − 2 b + 7

( a + 2 ) ( a − 5 ) ( a + 4 ) ( a + 2 ) ( a − 5 ) ( a + 4 )

( 3 p + 1 ) ( p + 6 ) ( p + 8 ) ( 3 p + 1 ) ( p + 6 ) ( p + 8 )

11 c − 12 ( c − 2 ) ( c + 3 ) 11 c − 12 ( c − 2 ) ( c + 3 )

5 x 2 + 26 x ( x + 4 ) ( x + 4 ) ( x + 6 ) 5 x 2 + 26 x ( x + 4 ) ( x + 4 ) ( x + 6 )

2 ( y 2 + 10 y − 2 ) ( y + 2 ) ( y + 8 ) 2 ( y 2 + 10 y − 2 ) ( y + 2 ) ( y + 8 )

2 m − 7 m + 2 2 m − 7 m + 2

4 a − 8 4 a − 8

R ( x ) = x + 8 x + 5 R ( x ) = x + 8 x + 5

R ( x ) = 2 x + 11 R ( x ) = 2 x + 11

x − 2 2 x x − 2 2 x

( x − 8 ) ( x − 5 ) 2 ( x − 8 ) ( x − 5 ) 2

z − 5 21 z + 21 z − 5 21 z + 21

x = 6 7 x = 6 7

b = 3 2 b = 3 2

ⓐ The domain is all real numbers except x ≠ 2 x ≠ 2 and x ≠ 4 . x ≠ 4 . ⓑ x = 1 , x = 6 x = 1 , x = 6 ⓒ ( 1 , 1 ) , ( 6 , 1 ) ( 1 , 1 ) , ( 6 , 1 )

l = V h w l = V h w

z = y + 5 + 7 x x z = y + 5 + 7 x x

1161 1161 calories

b = 9 ; x = 2 1 3 b = 9 ; x = 2 1 3

4 5 4 5 hour

301 301 mph

288 288 feet

97 97 tickets

( −4 , 3 ] ( −4 , 3 ]

[ −6 , 4 ) [ −6 , 4 )

( − ∞ , −2 ] ∪ [ 4 , ∞ ) ( − ∞ , −2 ] ∪ [ 4 , ∞ )

( − ∞ , 2 ) ∪ [ 5 , ∞ ) ( − ∞ , 2 ) ∪ [ 5 , ∞ )

ⓐ c ( x ) = 150 x + 100000 x c ( x ) = 150 x + 100000 x ⓑ More than 10,000 items must be produced to keep the average cost below $ 160 $ 160 per item.

Practice Test

a 3 b a 3 b

x + 3 3 x x + 3 3 x

n − m m + n n − m m + n

z = 1 2 z = 1 2

[ −3 , 6 ) [ −3 , 6 )

( − ∞ , 0 ) ∪ ( 0 , 4 ] ∪ [ 6 , ∞ ) ( − ∞ , 0 ) ∪ ( 0 , 4 ] ∪ [ 6 , ∞ )

R ( x ) = 1 ( x + 2 ) ( x + 2 ) R ( x ) = 1 ( x + 2 ) ( x + 2 )

y = 81 16 y = 81 16

Oliver’s dad would take 4 4 5 4 4 5 hours to split the logs himself.

The distance between Dayton and Columbus is 64 miles.

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• Authors: Lynn Marecek
• Publisher/website: OpenStax
• Book title: Intermediate Algebra
• Publication date: Mar 14, 2017
• Location: Houston, Texas
• Book URL: https://openstax.org/books/intermediate-algebra/pages/1-introduction
• Section URL: https://openstax.org/books/intermediate-algebra/pages/chapter-7

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Math 8 7.1 Combine Like Terms

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This worksheet accompanies Math 8 Lesson 7.1 Combine Like Terms written by Alex Benn using the concepts described in his book Tenacious-Teaching: Uniting Our Superpowers to Save Our Classrooms and on his website: Tenacious-Teaching.com. The problems are in order from easy for most to challenging for all. Answers are not included. Those are intended to be provided by students under the skilled guidance of a classroom teacher.

MATH 8 - Unit 7 Simplify and Solve Multi-Step Equations

7.1 Combine Like Terms

7.2 Solve Equations that Require Combining Like Terms

7.3 Distributive Property

7.4 Simplify More Complicated Expressions

7.5 Solve Equations that Require Distributive Property

7.6 Solve Equations with Variables on Both Sides

7.7 One, Infinite or No Solution

Review Unit 7

Test Unit 7

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Number line.

• -x+3\gt 2x+1
• (x+5)(x-5)\gt 0
• 10^{1-x}=10^4
• \sqrt{3+x}=-2
• 6+11x+6x^2+x^3=0
• factor\:x^{2}-5x+6
• simplify\:\frac{2}{3}-\frac{3}{2}+\frac{1}{4}
• x+2y=2x-5,\:x-y=3
• How do you solve algebraic expressions?
• To solve an algebraic expression, simplify the expression by combining like terms, isolate the variable on one side of the equation by using inverse operations. Then, solve the equation by finding the value of the variable that makes the equation true.
• What are the basics of algebra?
• The basics of algebra are the commutative, associative, and distributive laws.
• What are the 3 rules of algebra?
• The basic rules of algebra are the commutative, associative, and distributive laws.
• What is the golden rule of algebra?
• The golden rule of algebra states Do unto one side of the equation what you do to others. Meaning, whatever operation is being used on one side of equation, the same will be used on the other side too.
• What are the 5 basic laws of algebra?
• The basic laws of algebra are the Commutative Law For Addition, Commutative Law For Multiplication, Associative Law For Addition, Associative Law For Multiplication, and the Distributive Law.

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• High School Math Solutions – Systems of Equations Calculator, Elimination A system of equations is a collection of two or more equations with the same set of variables. In this blog post,...

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