Chapter 1.6, Problem 1LC

Solution

To solve the equation $\left|-6x\right|=24$ and check the answer.

  $-4\text{ and }4$

Given:

The equation, $\left|-6x\right|=24$ .

Concept Used:

• The opposite operation of addition is subtraction and the opposite operation of subtraction is addition.
• The opposite operation of multiplication is division and the opposite operation of division is multiplication.
• Distributive property: $a\left(b+c\right)=a\cdot b+a\cdot c$
• The absolute value property: $\text{if }\left|x\right|=a,\text{then}x=\pm a$

Calculation:

In order to solve the given equation $\left|-6x\right|=24$ , use the absolute value property and isolate the variable on one side by performing the basic algebraic operations as shown below

  $\begin{array}{c}\left|-6x\right|=24\\ -6x=-24\text{and }-6x=24\\ \frac{-6x}{-6}=\frac{-24}{-6}\text{and }\frac{-6x}{-6}=\frac{24}{-6}\\ x=4\text{and }x=-4\end{array}$

Thus, the solution of the equation are $-4\text{ and }4$ .

In order to check the solution, substitute back $x=\pm 4$ into the given equation and show that the left side expression is equal to the right-side expression as shown below

  $\begin{array}{c}\left|-6x\right|=24\\ \left|-6\cdot \left(\pm 4\right)\right|=24\\ \left|\pm 24\right|=24\\ 24=24\text{True statement}\end{array}$

Thus, $x=\pm 4$ is the solution of the equation.