Question

select the expressions that are equivalent to $(-4q - 8) + (-2q - 7)$.
$(-8q - 4) + (-2q - 7)$
$-4q - 15 + -2q$
$-6q - 15$
$(-2q + -7) + (-4q + -8)$

Explanation:

Step1: Simplify the original expression

First, remove parentheses and combine like terms:
$$(-4q - 8) + (-2q - 7) = -4q -8 -2q -7$$
Combine the $q$ terms: $-4q -2q = -6q$
Combine constant terms: $-8 -7 = -15$
Result: $-6q -15$

Step2: Check Option 1: $(-8q - 4) + (-2q - 7)$

Simplify:
$$-8q -4 -2q -7 = (-8q-2q)+(-4-7) = -10q -11$$
This is not equal to $-6q -15$.

Step3: Check Option 2: $-4q -15 + -2q$

Combine like terms:
$$-4q -2q -15 = -6q -15$$
This matches the simplified original expression.

Step4: Check Option 3: $-6q -15$

This is exactly the simplified form of the original expression, so it is equivalent.

Step5: Check Option 4: $(-2q + -7) + (-4q + -8)$

Rewrite and simplify:
$$-2q -7 -4q -8 = (-2q-4q)+(-7-8) = -6q -15$$
This matches the simplified original expression.

Answer:

• B. $-4q - 15 + -2q$
• C. $-6q - 15$
• D. $(-2q + -7) + (-4q + -8)$