Equivalent Expressions

Select all expressions that equal 6 + 3

• -6 + (-3)

• 6 - (-3)

• 6 + (3)

• 6 + (-3)

Select all expressions that equal 8 - 3

• 8 + (-3)

• 8 - (3)

• -8 + 3

• 8 - (-3)

Which of the following is equivalent to 9(5c + 4)?

• 45c + 36

• 81c

• 45c + 4

• 49c

Answer explanation

To distribute 9 to each term inside the parentheses, multiply 9 by 5c and 9 by 4. This gives us 45c + 36. Therefore, the correct equivalent expression is 45c + 36.

Find an equivalent expression for the given expression: 36x + 24

• 4(9x + 7)

• 4(9x + 8)

• 2(18x + 12)

• 12(3x + 2)

Answer explanation

To find an equivalent expression, we can factor out the greatest common factor. The GCF of 36 and 24 is 12. Factoring out 12, we get 12(3x + 2). This is equivalent to 2(18x + 12), which is the correct choice.

Which of the following is equivalent to 4(2x + 3)

• 8x + 12

• 8x + 3

• 8x - 12

• 20x

Answer explanation

To distribute 4 to each term inside the parentheses, multiply 4 by 2x and 4 by 3. This gives us 8x + 12. Therefore, the correct answer is 8x + 12.

Which answer choice is equivalent to:

• 3(4x+5)

• 3(4x-6)

• 4(4x-3)

• 4(3x-4)

• 8x-(4⋅4)+4x

Answer explanation

The correct answer choices are 4(3x-4) and 8x-(4⋅4)+4x. These choices are equivalent to 12x-16.

Which expression is equivalent to 7(3a + 4b)?

• 21a + 28b

• 10a + 11b

• 21a + 4b

• 10a + 28b

Answer explanation

To distribute 7 to both terms inside the parentheses, multiply 7 by 3a and 7 by 4b. This gives us 21a + 28b, which is equivalent to 7(3a + 4b). Therefore, the correct expression is 21a + 28b.

Simplify: 7(2a + b)

• 14a + 7b

• 72a + b

• 14a + 7

• 14ab

Answer explanation

To simplify 7(2a + b), distribute 7 to both terms inside the parentheses. This gives us 14a + 7b. Therefore, the correct choice is 14a + 7b.

Which expression is equivalent to 4(x + 6)?

• 4x + 6

• 4x + 24

• x + 24

• 10x + 24

Answer explanation

The expression 4(x + 6) can be simplified by distributing the 4 to both terms inside the parentheses. This gives us 4x + 24. Therefore, the correct choice is 4x + 24.

Which of the following is equivalent to 2(c - 8)?

• 2c - 16

• 2c + 16

• 2c - 8

• c - 16

Answer explanation

The expression 2(c - 8) simplifies to 2c - 16. Therefore, the correct choice is 2c - 16.