Question

Solve the following equation: $13x-5=\frac{3}{2}$

Answer 1

Solve linear equations in one variable.

Step 1: Add $5$ to both sides of the given equation.

$\begin{array}{rcl}13x-5+5& =& \frac{3}{2}+5\\ & \Rightarrow & 13x=\frac{3}{2}+\frac{5}{1}\\ & \Rightarrow & 13x=\frac{3}{2}+\frac{5\times 2}{1\times 2}\\ & \Rightarrow & 13x=\frac{3}{2}+\frac{10}{2}\\ & \Rightarrow & 13x=\frac{13}{2}\end{array}$

Step 2: Divide both sides by $13$.

$\begin{array}{rcl}\frac{13x}{13}& =& \frac{13}{2}\times \frac{1}{13}\\ & \Rightarrow & x=\frac{1}{2}\end{array}$

Hence, the solution of the equation $13x-5=\frac{3}{2}$ is $x=\frac{1}{2}$.