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: Recall the distributive property

The distributive property states that \(a(b - c)=ab - ac\). For the expression \(-7(9x - 5)\), we need to distribute \(-7\) to both terms inside the parentheses. So step 1 is to distribute \(-7\), which means option A is correct.

Step2: Apply the distributive property

Using the distributive property \(a(b - c)=ab - ac\), here \(a=-7\), \(b = 9x\) and \(c = 5\). So \(-7(9x-5)=-7\times9x-(-7)\times5\). Calculating each term: \(-7\times9x=-63x\) and \(-(-7)\times5 = + 35\) (because multiplying two negative numbers gives a positive number). So \(-7(9x - 5)=-63x + 35\), which means option D is correct.

Now let's check the other options:

• Option B: We don't add \(-7\) and \(-5\) first, we use the distributive property, so B is wrong.
• Option C: When we distribute \(-7\) to \(-5\), we should get \(+35\) (since \(-7\times(-5) = 35\)), not \(-35\), so C is wrong.
• Option E: The coefficient of \(x\) should be \(-63\) (since \(-7\times9=-63\)) and the constant term should be \(+35\), so E is wrong.

Answer:

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