Question

solve for w.
4(w + 5) = -2(7w - 4) + 4w
simplify your answer as much as possible.
w =

Explanation:

Step1: Expand both sides

Using the distributive property \(a(b + c)=ab+ac\), we expand the left - hand side: \(4(w + 5)=4w+20\).
For the right - hand side, we have \(-2(7w - 4)+4w=-14w + 8+4w\).
So the equation becomes \(4w+20=-14w + 8+4w\).

Step2: Combine like terms on the right - hand side

Combine the \(w\) terms on the right: \(-14w+4w=-10w\).
The equation is now \(4w + 20=-10w+8\).

Step3: Add \(10w\) to both sides

\(4w+10w + 20=-10w+10w+8\), which simplifies to \(14w+20 = 8\).

Step4: Subtract 20 from both sides

\(14w+20 - 20=8 - 20\), so \(14w=-12\).

Step5: Divide both sides by 14

\(w=\frac{-12}{14}\), and simplify the fraction by dividing numerator and denominator by 2: \(w =-\frac{6}{7}\).

Answer:

\(-\frac{6}{7}\)