Question

Find the value of the variable.

$7-z=13$

Short answer

The value of the variable is $z=-5$.

Step-by-step solution

Step 1. Subtract 7.

To find the value of variable in the equation $7-z=13$, subtract 7 from both sides of the equation.

$7-z-\left(7\right)=13-\left(7\right)$

Step 2. Collect like terms.

Remove all the brackets and collect the like terms.

$7-7-z=13-7$

Step 3. Simplify the equation.

To further simplify, combine the like terms.

$$\begin{gathered} 7-7-z=13-7 \\ 0-z=5 \\ -z=5 \end{gathered}$$

Step 4. Multiply by -1.

In order to obtain $z$, multiply the equation $-z=5$from both sides with $-1$.

$\begin{array}{c}-z\times \left(-1\right)=5\times \left(-1\right)\\ z=-5\end{array}$

Step 5. Verify the value.

In order to verify the value of z, substitute -5 for z into the equation $7-z=13$.

$$\begin{gathered} 7-\left(-5\right)=13 \\ 7+5=13 \\ 13=13\text{True} \end{gathered}$$

Hence, the value of the variable is $z=-5$.