Question

solve for w.
-9(w+8)=-4w-37
simplify your answer as much as possible.

Explanation:

Step1: Distribute -9

Using the distributive property \(a(b + c)=ab+ac\), we distribute \(-9\) to \(w\) and \(8\):
\(-9(w + 8)=-9w-72\)
So the equation becomes \(-9w - 72=-4w-37\).

Step2: Add 9w to both sides

To get all the \(w\) terms on one side, we add \(9w\) to both sides of the equation:
\(-9w - 72+9w=-4w-37 + 9w\)
Simplifying both sides, we have \(-72 = 5w-37\).

Step3: Add 37 to both sides

To isolate the term with \(w\), we add \(37\) to both sides:
\(-72 + 37=5w-37 + 37\)
Calculating the left side: \(-35 = 5w\).

Step4: Divide by 5

To solve for \(w\), we divide both sides by \(5\):
\(\frac{-35}{5}=\frac{5w}{5}\)
Simplifying, we get \(w=-7\).

Answer:

\(w = -7\)