Chapter A, Problem 32E

To determine

To calculate: To solve the equation

Answer to Problem 32E

  $x=-2,-\frac{4}{3}$

Explanation of Solution

Given information: Equation is $\left|3x+5\right|=1$

Formula Used:

If $\left|x\right|=a$ , then $x=\pm a$

Calculation:

Equation is given as

  $\left|3x+5\right|=1$

On solving,

  $3x+5=\pm 1$

Case1: When $3x+5=1$

  $\begin{array}{l}3x+5=1\\ 3x=1-5\\ 3x=-4\\ x=-\frac{4}{3}\end{array}$

Case 2: When $3x+5=-1$

  $\begin{array}{l}3x+5=-1\\ 3x=-1-5\\ 3x=-6\\ x=-\frac{6}{3}\\ x=-2\end{array}$

Thus, $x=-2,-\frac{4}{3}$

Conclusion:

Hence, $x=-2,-\frac{4}{3}$