Question

The number of solutions of an equation $\frac{2(2x-3)}{7}=6$ is

Answer 1

Given, the equation is $\frac{2(2x-3)}{7}=6.$

Step 1: Multiply both the sides by 7
$\Rightarrow \frac{2(2x-3)}{7}\times 7=6\times 7$
$\Rightarrow 2(2x-3)=42$

Step 2: Divide both the sides by 2
$\Rightarrow \frac{2(2x-3)}{2}=\frac{42}{2}$
$\Rightarrow 2x-3=21$

Step 3: Add 3 to both sides of the equation in order to remove the $3$ on the left hand side.
$\Rightarrow 2x-3+3=21+3$
$\Rightarrow 2x=24$

Step 4: Divide both the sides by 2
$\Rightarrow \frac{2x}{2}=\frac{24}{2}$
$\Rightarrow x=12$

Hence, number of solution of the equation $\frac{2(2x-3)}{7}=6$ is $1.$