Chapter 1.6, Problem 83PPSE

Solution

To solve the equation $\left|cx-d\right|=ab$ for x .

  $x=\frac{d\pm ab}{c}$

Given:

The equation $\left|cx-d\right|=ab$ .

Concept Used:

• If there is the strict inequality symbol $<\text{ or}>$ , then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$ , then use a bracket $\left[\right]$ on the interval
• To graph the endpoint with strict inequality $<\text{ or}>$ , use the open parenthesis or a hollow circle at that endpoint.
• To graph the endpoint with inequality symbol $\le \text{ or}\ge$ , use the bracket or a solid circle at that endpoint.
• Multiplying or dividing an inequality by a negative number reverse the inequality sign.
• The absolute value property: $\text{if }\left|x\right|=a,\text{then}x=\pm a$

Calculation:

In order to solve the given equation $\left|cx-d\right|=ab$ for x , use the absolute value property and simplify further as shown below

  $\begin{array}{c}\left|cx-d\right|=ab\\ cx-d=\pm ab\\ cx-d+d=\pm ab+d\\ cx=d\pm ab\\ \frac{cx}{c}=\frac{d\pm ab}{c}\\ x=\frac{d\pm ab}{c}\end{array}$

Thus, the required solution is $x=\frac{d\pm ab}{c}$ .