Chapter 1.3, Problem 54PPS

To determine

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

Answer to Problem 54PPS

The value of $x$ in the given equation is $3$ .

Explanation of Solution

Given information:

Given equation

  $\frac{1}{x}+\frac{1}{4}=\frac{7}{12}$

Calculation:

Consider the given equation,

  $\frac{1}{x}+\frac{1}{4}=\frac{7}{12}$

Now, solve the equation as shown,

  $\begin{array}{c}\frac{1}{x}+\frac{1}{4}=\frac{7}{12}\\ \frac{1}{x}+\frac{1}{4}-\frac{1}{4}=\frac{7}{12}-\frac{1}{4}\\ \frac{1}{x}=\frac{7-3}{12}\\ \frac{1}{x}=\frac{4}{12}\\ x=\frac{12}{4}\\ x=3\end{array}$

Now, check the result by back substitution.

  $\begin{array}{c}\frac{1}{3}+\frac{1}{4}=\frac{7}{12}\\ \frac{4+3}{12}=\frac{7}{12}\\ \frac{7}{12}=\frac{7}{12}\end{array}$

Which is true.

Hence, the value of $x$ in the given equation is $3$ .