Chapter 1, Problem 27SGR

To determine

To solve: the given equation for $x$ . Check the result.

Answer to Problem 27SGR

The value of $x$ in the given equation is $\frac{3}{2}$ .

Explanation of Solution

Given information:

Given equation

  $\frac{x}{6}+\frac{x}{3}=\frac{3}{4}$

Calculation:

Consider the given equation,

  $\frac{x}{6}+\frac{x}{3}=\frac{3}{4}$

Now, solve the equation as shown,

  $\begin{array}{c}\frac{x}{6}+\frac{x}{3}=\frac{3}{4}\\ \frac{x}{6}+\frac{2x}{6}=\frac{3}{4}\\ \frac{x+2x}{6}=\frac{3}{4}\\ \frac{3x}{6}=\frac{3}{4}\\ \frac{x}{2}=\frac{3}{4}\\ \frac{x}{2}\cdot 2=\frac{3}{4}\cdot 2\\ x=\frac{3}{2}\end{array}$

Now, check the result by back substitution.

  $\begin{array}{c}\frac{x}{6}+\frac{x}{3}=\frac{3}{4}\\ \frac{\frac{3}{2}}{6}+\frac{\frac{3}{2}}{3}=\frac{3}{4}\\ \frac{3}{12}+\frac{3}{6}=\frac{3}{4}\\ \frac{3}{12}+\frac{6}{12}=\frac{3}{4}\\ \frac{9}{12}=\frac{3}{4}\\ \frac{3}{4}=\frac{3}{4}\end{array}$

Which is true.

Hence, the value of $x$ in the given equation is $\frac{3}{2}$ .