Chapter B.5, Problem 1ES

To determine

To solve the equation for the variable using indicated operations.

Answer to Problem 1ES

The solution of the given equation is $x=\frac{1}{2}$ .

Explanation of Solution

Given information:

The given equation is -$\frac{x}{2}=\frac{1}{8}+\frac{x}{4}$ .

Calculation:

The given equationis $\frac{x}{2}=\frac{1}{8}+\frac{x}{4}$ .

Solving the above equation using basic arithmetic operations as follows-

  $\begin{array}{l}\frac{x}{2}=\frac{1}{8}+\frac{x}{4}\\ \Rightarrow \frac{x}{2}-\frac{x}{4}=\frac{1}{8}\{\text{bringing the variable on LHS of the equation}}\\ \Rightarrow \frac{2x-x}{4}=\frac{1}{8}\{\text{taking the LCD of fractions on LHS }}\\ \Rightarrow \frac{x}{4}=\frac{1}{8}\{\text{simplifying}}\\ \Rightarrow x=\frac{4}{8}\{\text{crossmulitplying}}\\ \Rightarrow x=\frac{1}{2}\end{array}$

The solution of the given equation is $x=\frac{1}{2}$ .