0. Review of College Algebra

Solving Linear Equations

0. Review of College Algebra

Solving Linear Equations

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Solving Linear Equations

Solving Linear Equations with Fractions

Categorizing Linear Equations

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Multiple Choice

Solve the Equation.

$3\left(2-5x\right)=4x+25$

Solve the equation.

$\frac92+\frac14\left(x+2\right)=\frac34x$

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation.

$5x+17=8x+12-3\left(x+4\right)$

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Multiple Choice

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation.

$\frac{x}{4}+\frac16=\frac{x}{3}$

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Multiple Choice

Solve the equation. Then state whether it is an identity, conditional, or inconsistent equation.

$-2\left(5-3x\right)+x=7x-10$

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Textbook Question

CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. The polynomial 2x⁵ - x + 4 is a trinomial of degree _________.

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Textbook Question

CONCEPT PREVIEW Work each problem. Match each polynomial in Column I with its factored form in Column II. I II a. x² + 10xy + 25y² A. (x + 5y) (x - 5y) b. x² - 10xy + 25y² B. (x + 5y)² c. x² - 25y² C. (x - 5y)² d. 25y² - x² D. (5y + x) (5y - x)

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Textbook Question

CONCEPT PREVIEW Work each problem. Match each polynomial in Column I with its factored form in Column II. I II a. 8x³ - 27 A. (3 - 2x) (9 + 6x + 4x²) b. 8x³ + 27 B. (2x - 3) (4x² + 6x + 9) c. 27 - 8x³ C. (2x + 3) (4x² - 6x + 9)

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Textbook Question

CONCEPT PREVIEW Which of the following is the correct factorization of x⁴ - 1? A. (x² - 1) (x² + 1) B. (x² + 1) (x + 1) (x - 1) C. (x² - 1)² D. (x - 1)² (x + 1)²

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Textbook Question

Simplify each expression. See Example 1. (-4x⁵) (4x²)

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Textbook Question

Simplify each expression. See Example 1. n⁶ • n⁴ • n

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Textbook Question

Simplify each expression. See Example 1. 9³ • 9⁵

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Textbook Question

Simplify each expression. See Example 1. (-3m⁴) (6m²) (-4m⁵)

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Textbook Question

Simplify each expression. See Example 1. (5x²y) (-3x³y⁴)

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Textbook Question

Simplify each expression. See Example 1. (½ mn) (8m²n²)

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Textbook Question

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. (2²)⁵

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Textbook Question

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. (-6x²)³

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Textbook Question

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. -(4m³n⁰)²

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Textbook Question

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. r⁸ ( —— )³ s²

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Textbook Question

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. -4m² ( ——— )⁴ tp²

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Textbook Question

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. x³y⁵ - ( ——— )⁰ z

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Textbook Question

Match each expression in Column I with its equivalent in Column II. See Example 3. I II. a. 6° A. 0 b. -6° B. 1 c. (-6)° C. -1 d. -(-6)° D. 6 E. -6

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Textbook Question

Add or subtract, as indicated. See Example 4. (5x² - 4x + 7) + (-4x² + 3x - 5)

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Textbook Question

Add or subtract, as indicated. See Example 4. 2(12y² - 8y + 6) - 4(3y² - 4y +2)

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Textbook Question

Add or subtract, as indicated. See Example 4. (6m⁴ - 3m² + m) - (2m³ + 5m² + 4m) + (m² - m)

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Textbook Question

Find each product. See Example 5. 4x² (3x³ + 2x² - 5x +1)

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Textbook Question

Find each product. See Example 5. (4r - 1) (7r + 2)

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Textbook Question

Find each product. See Example 5. (3x + 1) (2x - 7)

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Find each product. See Example 5. (2m + 3) (2m - 3)

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Textbook Question

Find each product. See Example 5. (4x² - 5y) (4x² + 5y)

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Textbook Question

Find each product. See Example 5. (4m + 2n)²

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Textbook Question

Find each product. See Example 5. (5r - 3t²)²

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Textbook Question

Find each product. See Example 5. (x + 1) (x + 1) (x - 1) (x - 1)

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Textbook Question

Find each product. See Example 5. (y + 2)³

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Textbook Question

Find each product. See Example 5. (2x + 5)³

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Textbook Question

Find each product. See Example 5. (q - 2)⁴

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Textbook Question

Factor each polynomial completely. See Example 6. 40ab - 16a

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Textbook Question

Factor each polynomial completely. See Example 6. 8x³y⁴ + 12x²y³ + 36xy⁴

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Textbook Question

Factor each polynomial completely. See Example 6. x² - 2x - 15

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Textbook Question

Factor each polynomial completely. See Example 6. 6a² - 11a + 4

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Textbook Question

Factor each polynomial completely. See Example 6. 4x² - 28x + 40

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Textbook Question

Factor each polynomial completely. See Example 6. 25s⁴ - 9t²

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Textbook Question

Factor each polynomial completely. See Example 6. 4m²p - 12mnp + 9n²p

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Textbook Question

Factor each polynomial completely. See Example 6. 8t³ + 125

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Textbook Question

Factor each polynomial completely. See Example 6. t⁴ - 1

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Textbook Question

Factor each polynomial completely. See Example 6. 6ar + 12br - 5as - 10bs

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Textbook Question

Give (a) the additive inverse and (b) the absolute value of each number. 6

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Textbook Question

Give (a) the additive inverse and (b) the absolute value of each number. -6⁄5

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Textbook Question

Give (a) the additive inverse and (b) the absolute value of each number. 0.16

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Textbook Question

Evaluate each expression. See Example 5. |-8|

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Textbook Question

Evaluate each expression. See Example 5. |3⁄2|

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Textbook Question

Evaluate each expression. See Example 5. -|5|

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Textbook Question

Evaluate each expression. See Example 5. -|-2|

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Textbook Question

Evaluate each expression. See Example 5. -|4.5|

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Textbook Question

CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. The numerical coefficient in the term -7yz² is ___________.

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Textbook Question

CONCEPT PREVIEW Evaluate each expression. 10³

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CONCEPT PREVIEW Evaluate each expression. 2 • 5 - 10 ÷ 2

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CONCEPT PREVIEW Evaluate each expression. 3a - 2b, for a = -2 and b = -1

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Textbook Question

CONCEPT PREVIEW Rewrite the expression -7(x - 4y) using the distributive property.

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Textbook Question

Find each sum or difference. See Example 1. -6 + (-13)

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Textbook Question

Find each sum or difference. See Example 1. -15 + 6

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Textbook Question

Find each sum or difference. See Example 1. 13 + (-4)

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Textbook Question

Find each sum or difference. See Example 1. -7⁄3 + 3⁄4

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Textbook Question

Find each sum or difference. See Example 1. -2.8 + 4.5

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Textbook Question

Find each sum or difference. See Example 1. 4 - 9

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Textbook Question

Find each sum or difference. See Example 1. -6 - 5

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Textbook Question

Find each sum or difference. See Example 1. 8 - (-13)

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Textbook Question

Find each sum or difference. See Example 1. -12.31 - (-2.13)

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Textbook Question

Find each sum or difference. See Example 1. 9⁄10 - ( -4⁄3)

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Textbook Question

Find each sum or difference. See Example 1. |-8 - 6|

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Find each sum or difference. See Example 1. -2 - |-4|

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Textbook Question

Find each product or quotient where possible. See Example 2. -8(-5)

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Find each product or quotient where possible. See Example 2. 5(-7)

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Find each product or quotient where possible. See Example 2. 4(0)

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Textbook Question

Find each product or quotient where possible. See Example 2. -5⁄2 ( 12⁄15 )

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Find each product or quotient where possible. See Example 2. -3⁄8 ( -24⁄9 )

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Textbook Question

Find each product or quotient where possible. See Example 2. -0.06(0.4)

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Textbook Question

Find each product or quotient where possible. See Example 2. -24 -4

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Textbook Question

Find each product or quotient where possible. See Example 2. 100 -25

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Textbook Question

Find each product or quotient where possible. See Example 2. 0 — -8

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Textbook Question

Find each product or quotient where possible. See Example 2. 5⁄0

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Textbook Question

Find each product or quotient where possible. See Example 2. -10⁄17 ÷ ( -12⁄5 )

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Textbook Question

Find each product or quotient where possible. See Example 2. -4⁄5 -3⁄5

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Textbook Question

Find each product or quotient where possible. See Example 2. 12⁄13 -4⁄3

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Textbook Question

Find each product or quotient where possible. See Example 2. 2𝝅 2⁄3 (Leave 𝝅 in the answer.)

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Textbook Question

Find each product or quotient where possible. See Example 2. -7.2 0.8

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Textbook Question

Find the given distances between points P, Q, R, and S on a number line, with coordinates -4, -1, 8, and 12, respectively. See Example 3. d (P, Q)

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Textbook Question

Find the given distances between points P, Q, R, and S on a number line, with coordinates -4, -1, 8, and 12, respectively. See Example 3. d (Q, R)

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Textbook Question

Concept Check Evaluate each exponential expression. a. 8² b. -8² c. (-8)² d. -(-8)²

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Textbook Question

Evaluate each expression. See Example 4. -2⁴

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Textbook Question

Evaluate each expression. See Example 4. (-2)⁴

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Textbook Question

Evaluate each expression. See Example 4. (-3)⁵

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Evaluate each expression. See Example 4. -2 • 3⁴

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Textbook Question

Evaluate each expression. See Example 5. 12 + 3 • 4

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Textbook Question

Evaluate each expression. See Example 5. 6 • 3 - 12 ÷ 4

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Textbook Question

Evaluate each expression. See Example 5. 10 + 30 ÷ 2 • 3

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Textbook Question

Evaluate each expression. See Example 5. 5 - 7 • 3 - (-2)³

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Textbook Question

Evaluate each expression. See Example 5. 18 - 4² + 5 - (3 - 7)

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Textbook Question

Evaluate each expression. See Example 5. -4(9 - 8) + (-7) (2)³

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Textbook Question

Evaluate each expression. See Example 5. -8 + (-4) (-6) ÷ 12 4 - (-3)

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Textbook Question

Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. 3p - 2r

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Textbook Question

Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. -p² - 7q + r

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Textbook Question

Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. q + r q + p

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Textbook Question

Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. 5r ——— 2p - 3r

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Textbook Question

Evaluate each expression for p = -4, q = 8, and r = -10. See Example 6. -(p + 2)² - 3r —————— 2 - q

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Textbook Question

Identify the property illustrated in each statement. Assume all variables represent real numbers. 6 • 12 + 6 • 15 = 6(12 + 15)

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Textbook Question

Identify the property illustrated in each statement. Assume all variables represent real numbers. 1 (t - 6) • ( ——— ) = 1, if t - 6 ≠ 0 t - 6

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Textbook Question

Identify the property illustrated in each statement. Assume all variables represent real numbers. (7.5 - y) + 0 = 7.5 - y

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Textbook Question

Identify the property illustrated in each statement. Assume all variables represent real numbers. 5(t + 3) = (t + 3) • 5

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Textbook Question

Identify the property illustrated in each statement. Assume all variables represent real numbers. 1 1 (5x) ( — ) = 5 ( x • — ) x x

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Textbook Question

Identify the property illustrated in each statement. Assume all variables represent real numbers. 5 + √3 is a real number.

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Textbook Question

Rewrite each expression using the distributive property and simplify, if possible. See Example 7. 2(m + p)

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Textbook Question

Rewrite each expression using the distributive property and simplify, if possible. See Example 7. -12(x - y)

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Rewrite each expression using the distributive property and simplify, if possible. See Example 7. -(2d - f)

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Rewrite each expression using the distributive property and simplify, if possible. See Example 7. 5k + 3k

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Rewrite each expression using the distributive property and simplify, if possible. See Example 7. 7r - 9r

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Textbook Question

Rewrite each expression using the distributive property and simplify, if possible. See Example 7. a + 7a

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Textbook Question

Rewrite each expression using the distributive property and simplify, if possible. See Example 7. x + x

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Rewrite each expression using the distributive property and simplify, if possible. See Example 7. 2 (x - 3y + 2z)

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Rewrite each expression using the distributive property and simplify, if possible. See Example 7. 3 16 32 40 —— ( —— y + —— z - —— ) 8 9 27 9

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Textbook Question

Simplify each expression. See Example 8. -12y + 4y + 3y + 2y

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Textbook Question

Simplify each expression. See Example 8. -6p + 5 - 4p + 6 + 11p

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Textbook Question

Simplify each expression. See Example 8. 3(k + 2) - 5k + 6 + 3

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Textbook Question

Simplify each expression. See Example 8. 10 - (4y + 8)

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Textbook Question

Simplify each expression. See Example 8. 10x (3)(y)

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Simplify each expression. See Example 8. -2⁄3 (12w) (7z)

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Simplify each expression. See Example 8. 3(m - 4) - 2(m + 1)

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Textbook Question

Simplify each expression. See Example 8. 0.25(8 + 4p) - 0.5(6 + 2p)

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