Chapter 3, Problem 22CT

To determine

To solve: the given equation and to verify the solution.

Answer to Problem 22CT

The solution is $t=0\text{ or }10$ .

Explanation of Solution

Given information:

The given equation is $4|5-t|=20$

Calculation:

Solve the inequality

  $\begin{array}{l}4|5-t|=20\text{ given}\\ |5-t|=5\\ 5-t=\pm 5\\ 5-t=5\Rightarrow t=0\\ 5-t=-5\Rightarrow t=10\\ t=0\text{ or }10\end{array}$

Verify the solution

  $\begin{array}{l}4|5-t|=20\text{ given}\\ 4|5-0|=20\text{ put t}=0\\ 4\left|5\right|=20\\ 20=20\text{ true}\\ 4|5-t|=20\text{ given}\\ 4|5-10|=20\text{ put t}=10\\ 4|-5|=20\\ 20=20\text{ true}\end{array}$

Hence, the solution is $t=0\text{ or }10$ .