Chapter 8.5, Problem 35E

To determine

To solve:

The given equation. Check your solution.

Answer to Problem 35E

The solution of our given equation would be $z=4$ .

Explanation of Solution

Given:

An equation: $-20=4\left(7-3z\right)$ .

Calculation:

To solve our given equation, we use opposite operations as shown below:

  $\begin{array}{l}-20=4\left(7-3z\right)\left(\text{Given equation}\right)\\ 4\left(7-3z\right)=-20\left(\text{Switching sides}\right)\\ \frac{4\left(7-3z\right)}{4}=\frac{-20}{4}\left(\text{Dividing both sides by }4\right)\\ 7-3z=-5\\ 7-7-3z=-5-7\left(\text{Subtracting 7 from both sides}\right)\\ -3z=-12\\ \frac{-3z}{-3}=\frac{-12}{-3}\left(\text{Dividing both sides by }-3\right)\\ z=4\end{array}$

Let us verify our answer by substituting $z=4$ in our original equation.

  $\begin{array}{l}-20=4\left(7-3z\right)\left(\text{Given equation}\right)\\ -20=4\left(7-3(4)\right)\left(\text{Substituting }z=4\right)\\ -20=4\left(7-12\right)\\ -20=4\left(-5\right)\\ -20=-20\end{array}$

Since both sides of equation are equal, therefore,

  $z=4$ is a solution of our given equation.