Chapter P, Problem 38RE

Solution

The solution of the given equation.

  $x=-\frac{9}{5}$

Given information:

The equation given is:

  $\frac{x-2}{3}+\frac{x+5}{2}=\frac{1}{3}$ .

Formula used:

To solve an equation, follow the steps below:

1. Take all the terms of variable on one side of the equation and rest on other side of the equals side of the equation.
2. Simplify the both sides.
3. Make the coefficient of variable 1.

Calculation:

In order to solve the given equation:

  $\frac{x-2}{3}+\frac{x+5}{2}=\frac{1}{3}$

First solve the left side, as:

  $\begin{array}{c}\frac{x-2}{3}+\frac{x+5}{2}=\frac{1}{3}\\ \frac{2\left(x-2\right)+3\left(x+5\right)}{6}=\frac{1}{3}\\ \frac{2x-4+3x+15}{6}=\frac{1}{3}\\ \frac{5x+11}{6}=\frac{1}{3}\\ \frac{5x}{6}+\frac{11}{6}=\frac{1}{3}\end{array}$

Now take the variables on one side of the equals sign in equation and rest on other side and simplify as:

  $\begin{array}{c}\frac{5x}{6}+\frac{11}{6}=\frac{1}{3}\\ \frac{5x}{6}+\frac{11}{6}-\frac{11}{6}=\frac{1}{3}-\frac{11}{6}\\ \frac{5x}{6}+0=\frac{2-11}{6}\\ \frac{5x}{6}=\frac{-9}{6}\end{array}$

Multiply both sides with 6:

  $\begin{array}{c}\frac{5x}{6}\times 6=\frac{-9}{6}\times 6\\ 5x=-9\end{array}$

Now in order to make the coefficient of variable x 1, divide both side with 5, as

  $\begin{array}{c}\frac{5x}{5}=\frac{-9}{5}\\ x=-\frac{9}{5}\end{array}$

Thus, solution of given equation is:

  $x=-\frac{9}{5}$