Question

solve for w. -17w + w + 13w + 16w - 20 = 19 w = \boxed{} submit

Explanation:

Step1: Combine like terms

First, we combine the terms with \( w \) on the left - hand side of the equation \(-17w + w+13w + 16w-20 = 19\).
\(-17w+w + 13w+16w=(-17 + 1+13 + 16)w\)
\(-17+1=-16\), \(-16 + 13=-3\), \(-3+16 = 13\). So, \((-17 + 1+13 + 16)w=13w\). The equation becomes \(13w-20 = 19\).

Step2: Isolate the term with \( w \)

Add 20 to both sides of the equation \(13w-20 = 19\) to isolate the term with \( w \).
\(13w-20 + 20=19 + 20\)
Simplifying both sides, we get \(13w=39\).

Step3: Solve for \( w \)

Divide both sides of the equation \(13w = 39\) by 13.
\(\frac{13w}{13}=\frac{39}{13}\)
Simplifying, we find that \(w = 3\).

Answer:

\(w = 3\)