Final answer:
The equivalent expression to -4(7q + 4) + 6q is found by using the distributive property and combining like terms, resulting in -22q - 16, which matches option (c) when terms are rearranged.
Step-by-step explanation:
The student has asked which expression is equivalent to -4(7q + 4) + 6q. To find the equivalent expression, first apply the distributive property by multiplying -4 with each term inside the parentheses, and then add 6q.
-4 × 7q = -28q
-4 × 4 = -16
So, the expression becomes -28q - 16 + 6q. Combine like terms:
-28q + 6q = -22q
Therefore, the expression simplifies to -22q - 16, which is not directly in the form of any of the provided options. However, we can rearrange the terms in option (c) to see if it matches the simplified expression.
Option (c) is -4(4 + 7q), which distributes to:
-4 × 4 = -16
-4 × 7q = -28q
When you rearrange the terms inside the parentheses of option (c), you get -4(7q + 4). So, option (c) is indeed equivalent to the original expression given in the question.