Question

solve and check
\frac{2}{3}z = 6
the solution is z = \square
(simplify your answer.)

Explanation:

Step1: Multiply both sides by 3/2

To solve for \( z \) in the equation \( \frac{2}{3}z = 6 \), we multiply both sides by the reciprocal of \( \frac{2}{3} \), which is \( \frac{3}{2} \). So we have \( \frac{3}{2} \times \frac{2}{3}z = 6 \times \frac{3}{2} \).

Step2: Simplify both sides

On the left side, \( \frac{3}{2} \times \frac{2}{3} = 1 \), so we get \( z = \frac{6\times3}{2} \). Calculating the right side, \( 6\times3 = 18 \), and \( \frac{18}{2} = 9 \).

Answer:

\( z = 9 \)