Question

Justify each step.

$\frac{z+7}{3}=-11$

$z+7=-33$

$z=-40$

Short answer

$\frac{z+7}{3}=-11$Given

$z+7=-33$Multiplication property of equality

$z=-40$Subtraction property of equality

Step-by-step solution

Step 1. Apply the multiplication property of equality.

If $a=b$, then $ca=cb$.

Step 2. Description of step.

Multiply each side of $\frac{z+7}{3}=-11$by 3 and simplify.

$\begin{array}{c}3\times \frac{z+7}{3}=3\times \left(-11\right)\\ z+7=-33\end{array}$

Step 3. Apply the subtraction property of equality.

If $a=b$and $c=d$, then $a-c=b-d$.

Step 4. Description of step.

Subtract 7 from each side of the equation obtained in step 2 to find the value of z.

$\begin{array}{c}z+7-7=-33-7\\ z=-40\end{array}$

Therefore, the value of z is $-40$.