Chapter 1, Problem 7CR

To determine

To calculate:

The solution of the following equation and verify it:

  $-4\left(2z+6\right)-12=4$

Answer to Problem 7CR

The solution of $-4\left(2z+6\right)-12=4$ is $-5$

Explanation of Solution

Given information:

  $-4\left(2z+6\right)-12=4$

Calculation:

The given equation is:

  $-4\left(2z+6\right)-12=4$

Add $12$ on both sides of above equation:

  $\begin{array}{l}-4\left(2z+6\right)-12+12=4+12\\ -4\left(2z+6\right)=16\end{array}$

Divide by $-4$ on both sides of above equation:

  $\begin{array}{l}-4\left(2z+6\right)=16\\ \frac{-4}{-4}\left(2z+6\right)=\frac{16}{-4}\\ 2z+6=-4\end{array}$

Subtract $6$ from both sides of above equation:

  $\begin{array}{l}2z+6-6=-4-6\\ 2z=-10\end{array}$

Divide by $2$ :

  $\begin{array}{l}\frac{2}{2}z=\frac{-10}{2}\\ z=-5\end{array}$

Hence, the solution of

  $-4\left(2z+6\right)-12=4$ is $-5$

Check for the solution: put $z=-5$ in $-4\left(2z+6\right)-12=4$ :

  $\begin{array}{l}-4\left(2z+6\right)-12=4\\ -4\left(2\left(-5\right)+6\right)-12=4\\ -4\left(-4\right)-12=4\\ 16-12=4\\ 4=4\end{array}$

Both sides are equal. Hence the solution is correct or verified.