Chapter EP, Problem 1.4.22EP

To determine

To solve: The equation $\left|3t+6\right|+9=30$ .

Answer to Problem 1.4.22EP

The solutions of the equation $\left|3t+6\right|+9=30$ are $\left(5,-9\right)$ .

Explanation of Solution

Given:

The equation is $\left|3t+6\right|+9=30$ .

Calculation:

Remove the mod from the equation.

  $\begin{array}{c}\left|3t+6\right|+9-9=30-9\\ \left|3t+6\right|=21\\ 3t+6=\pm 21\end{array}$

Simplify the equation $3t+6=21$ .

  $\begin{array}{c}3t+6-6=21-6\\ 3t=15\\ t=\frac{15}{3}\\ =5\end{array}$

Simplify the equation $3t+6=-21$ .

  $\begin{array}{c}3t+6-6=-21-6\\ 3t=-27\\ t=-\frac{27}{3}\\ =-9\end{array}$

Therefore, the solutions of the equation $\left|3t+6\right|+9=30$ are $\left(5,-9\right)$ .

To check the solution, substitute these values in the original equation.

Substitute $t=5$ in the equation $\left|3t+6\right|+9=30$ .

  $\begin{array}{c}\left|3\left(5\right)+6\right|+9=30\\ \left|15+6\right|+9=30\\ 30=30\\ \text{LHS}=\text{RHS}\end{array}$

Substitute $t=-9$ in the equation $\left|3t+6\right|+9=30$ .

  $\begin{array}{c}\left|3\left(-9\right)+6\right|+9=30\\ \left|-27+6\right|+9=30\\ 30=30\\ \text{LHS}=\text{RHS}\end{array}$

So, the solutions $\left(5,-9\right)$ are correct.

Therefore, the solutions of the equation $\left|3t+6\right|+9=30$ are $\left(5,-9\right)$ .