Chapter 4 Mastering Algebraic Expressions

Evaluate: 3(x + 4) when x = 2.

• 6

• 12

• 24

• 18

Answer explanation

To evaluate 3(x + 4) when x = 2, substitute 2 for x: 3(2 + 4) = 3(6) = 18. Thus, the correct answer is 18.

Combine like terms: 5x + 3x - 2 + 7.

• 8x - 2

• 8x + 5

• 6x + 5

• 5x + 9

Answer explanation

To combine like terms, add the coefficients of x: 5x + 3x = 8x. Then, combine the constants: -2 + 7 = 5. Thus, the final expression is 8x + 5, which matches the correct answer.

Use the distributive property: 4(2y + 3).

• 8y + 6

• 4y + 3

• 8y + 12

• 6y + 9

Answer explanation

To apply the distributive property, multiply 4 by each term inside the parentheses: 4 * 2y = 8y and 4 * 3 = 12. Thus, 4(2y + 3) = 8y + 12, making '8y + 12' the correct answer.

Simplify: 6a + 4b - 2a + 3b.

• 4a + 7b

• 8a + 4b

• 2a + 5b

• 6a + 7b

Answer explanation

Combine like terms: (6a - 2a) + (4b + 3b) = 4a + 7b. Thus, the simplified expression is 4a + 7b, which is the correct choice.

Evaluate: 2(3 + y) when y = 5.

• 12

• 16

• 20

• 10

Answer explanation

To evaluate 2(3 + y) when y = 5, substitute y: 2(3 + 5) = 2(8) = 16. Thus, the correct answer is 16.

Combine like terms: 7m - 2n + 3m + n.

• 4m - 3n

• 10m - n

• 10m + 2n

• 5m - n

Answer explanation

To combine like terms, add the coefficients of 'm' and 'n'. For 'm': 7m + 3m = 10m. For 'n': -2n + n = -n. Thus, the result is 10m - n, which matches the correct answer.

Use the distributive property: 5(3x - 2).

• 15x - 10

• 15 - 10x

• 3(5x - 2)

• 5x - 2

Answer explanation

Using the distributive property, multiply 5 by each term inside the parentheses: 5 * 3x = 15x and 5 * -2 = -10. Thus, 5(3x - 2) simplifies to 15x - 10, which is the correct answer.

Solve for y: 3(y - 4) = 12.

• 4

• 12

• 8

• 0

Answer explanation

To solve for y, first distribute: 3y - 12 = 12. Then, add 12 to both sides: 3y = 24. Finally, divide by 3: y = 8. Thus, the correct answer is 8.

Simplify: 8p - 3p + 2p + 5.

• 7p + 5

• 7p - 5

• 10p + 5

• 5p + 8

Answer explanation

Combine like terms: 8p - 3p + 2p = (8 - 3 + 2)p = 7p. The constant term remains 5. Thus, the simplified expression is 7p + 5, which matches the correct answer.

Evaluate: 4(a + 2) when a = 3.

• 12

• 24

• 16

• 20

Answer explanation

To evaluate 4(a + 2) when a = 3, substitute 3 for a: 4(3 + 2) = 4(5) = 20. Thus, the correct answer is 20.