Question

which two statements are correct when simplifying this expression?
-7(9x - 5)
a first, distribute -7.
b first, calculate -7 + (-5).
c -7(9x - 5) = -63x - 35.
d -7(9x - 5) = -63x + 35.
e -7(9x - 5) = 63x - 35.

Explanation:

Step1: Analyze Option A

To simplify \(-7(9x - 5)\), the distributive property ( \(a(b - c)=ab - ac\) ) is used. So first, we distribute \(-7\) to both terms inside the parentheses. So option A is correct.

Step2: Analyze Option B

There is no addition of \(-7\) and \(-5\) in the simplification of \(-7(9x - 5)\). The operation is distribution, not addition of these constants. So option B is incorrect.

Step3: Analyze Option C

Using the distributive property: \(-7\times9x=-63x\) and \(-7\times(-5) = 35\) (because multiplying two negative numbers gives a positive number). So \(-7(9x - 5)=-63x + 35\), not \(-63x-35\). So option C is incorrect.

Step4: Analyze Option D

As calculated above, \(-7\times9x=-63x\) and \(-7\times(-5) = 35\), so \(-7(9x - 5)=-63x + 35\). So option D is correct.

Step5: Analyze Option E

\(-7\times9x=-63x\) not \(63x\), so option E is incorrect.

Answer:

A. First, distribute \(-7\).
D. \(-7(9x - 5) = -63x + 35\).