Chapter 1.4, Problem 58PPSE

Solution

To solve the equation $\frac{a}{b}\left(2x-12\right)=\frac{c}{d}$ for x .

  $x=\frac{1}{2}\left(\frac{bc}{ad}+12\right)$

Given:

The equation, $\frac{a}{b}\left(2x-12\right)=\frac{c}{d}$ .

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: $a\left(b+c\right)=a\cdot b+a\cdot c$

Calculation:

In order to solve the given equation $\frac{a}{b}\left(2x-12\right)=\frac{c}{d}$ for x , isolate the variable on one side by performing the basic algebraic operations as shown below

  $\begin{array}{c}\frac{a}{b}\left(2x-12\right)=\frac{c}{d}\\ \frac{b}{a}\cdot \frac{a}{b}\left(2x-12\right)=\frac{b}{a}\cdot \frac{c}{d}\\ \left(2x-12\right)=\frac{bc}{ad}\\ 2x-12+12=\frac{bc}{ad}+12\\ 2x=\frac{bc}{ad}+12\\ \frac{1}{2}\cdot 2x=\frac{1}{2}\cdot \left(\frac{bc}{ad}+12\right)\\ x=\frac{1}{2}\left(\frac{bc}{ad}+12\right)\end{array}$

Thus, the required solution is $x=\frac{1}{2}\left(\frac{bc}{ad}+12\right)$ .