Question

solve for w.
-18w + 5(-13w - 2) = 8(-2w - 18)
w = □

Explanation:

Step1: Expand both sides

First, expand the expressions using the distributive property \(a(b + c)=ab+ac\).
\(-18w+5\times(-13w)+5\times(-2)=8\times(-2w)+8\times(-18)\)
\(-18w - 65w-10=-16w - 144\)

Step2: Combine like - terms on the left - hand side

Combine the \(w\) terms on the left - hand side: \((-18w-65w)-10=-16w - 144\)
\(-83w-10=-16w - 144\)

Step3: Add \(83w\) to both sides

To get all \(w\) terms on one side, add \(83w\) to both sides: \(-83w + 83w-10=-16w+83w - 144\)
\(-10 = 67w-144\)

Step4: Add 144 to both sides

Add 144 to both sides to isolate the term with \(w\): \(-10 + 144=67w-144 + 144\)
\(134 = 67w\)

Step5: Solve for \(w\)

Divide both sides by 67: \(\frac{134}{67}=\frac{67w}{67}\)
\(w = 2\)

Answer:

\(2\)