Chapter 11.5, Problem 2P

Solve each equation. Check your solution.

$\frac{8}{c+2}-6=\frac{4}{c+2}$

To determine

To solve the equation and check the solutions.

Answer to Problem 2P

The solution is $c=-\frac{4}{3}$ .

Explanation of Solution

Given information:

The given equation is:

  $\frac{8}{c+2}-6=\frac{4}{c+2}$

Calculation:

The solution can be obtained by:

  $\begin{array}{l}\frac{8}{c+2}-6=\frac{4}{c+2}\\ \frac{8-6\left(c+2\right)}{c+2}=\frac{4}{c+2}\\ \frac{8-6c-12}{c+2}=\frac{4}{c+2}\\ \frac{-4-6c}{c+2}=\frac{4}{c+2}\\ -4-6c=\frac{4\left(c+2\right)}{c+2}\\ -4-6c=4\\ 6c=-4-4\\ c=-\frac{8}{6}\\ c=-\frac{4}{3}\end{array}$

Hence, the solution is $c=-\frac{4}{3}$ .

The solution can be checked by:

  $\begin{array}{l}\frac{8}{c+2}-6=\frac{4}{c+2}\\ \frac{8}{-\frac{4}{3}+2}-6=\frac{4}{-\frac{4}{3}+2}\\ \frac{8\times 3}{2}-6=\frac{4\times 3}{2}\\ \frac{24}{2}-6=\frac{12}{2}\\ \frac{12}{2}=\frac{12}{2}\end{array}$

The solution is correct.