Question

Find the value of the variable.

$7y=180-2z$

Short answer

The value of the variable is $\mathit{z}\mathbf{=}\mathbf{20}$.

Step-by-step solution

Step 1. Add 2z.

First add 2z to both sides of the equation $7y=180-2z$.

$7y+\left(2z\right)=180-2z+\left(2z\right)$

Step 2. Combine the like terms.

To further simplify open the brackets and combine the like terms.

$\begin{array}{l}7y+2z=180-2z+2z\\ 9y=180\end{array}$

Step 3. Divide by 9.

Divide both sides of the equation$9y=180$ by 9 and cancel the common factors of 9 on both sides.

$\begin{array}{l}\frac{9y}{9}=\frac{180}{9}\\ y=\frac{9\times 20}{9}\\ y=20\end{array}$

Step 4. Verify the value.

In order to verify the value of y, substitute 20 for y into the equation $7y=180-2z$.

$\begin{array}{l}7\times 20=180-2\times 20\\ 140=180-40\\ 140=140\text{True}\end{array}$

Hence, the value of the variable is $y=20$.