Question

solve for w.
\frac{7}{2}w = 14
simplify your answer as much as possible.

Explanation:

Step1: Multiply both sides by 2/7

To isolate \( w \), we multiply both sides of the equation \( \frac{7}{2}w = 14 \) by the reciprocal of \( \frac{7}{2} \), which is \( \frac{2}{7} \).
\[
\frac{2}{7} \times \frac{7}{2}w = \frac{2}{7} \times 14
\]

Step2: Simplify both sides

The left side simplifies to \( w \) because \( \frac{2}{7} \times \frac{7}{2} = 1 \). For the right side, we calculate \( \frac{2}{7} \times 14 \). We can rewrite 14 as \( \frac{14}{1} \), then multiply the numerators and denominators: \( \frac{2 \times 14}{7 \times 1} = \frac{28}{7} = 4 \).
\[
w = 4
\]

Answer:

\( w = 4 \)