Question

Solve for $x:$
$\frac{x}{3}+\frac{1}{3}=5$

• A. $x=14$
• B. $x=3$
• C. $x=15$
• D. $x=5$

Answer 1

The correct option is A $x=14$

Given, the equation is $\frac{x}{3}+\frac{1}{3}=5.$

Step 1: Subtract both sides of the equation by $\frac{1}{3}$ in order to remove the $\frac{1}{3}$ on the left hand side.
$\Rightarrow \frac{x}{3}+\frac{1}{3}-\frac{1}{3}=5-\frac{1}{3}$
$\Rightarrow \frac{x}{3}=5-\frac{1}{3}(\because \frac{1}{3}-\frac{1}{3}=0)$
$\Rightarrow \frac{x}{3}=\frac{5\times 3}{1\times 3}-\frac{1}{3}\left(\text{making the denominators equal for}5\text{and}\frac{1}{3}\right)$
$\Rightarrow \frac{x}{3}=\frac{15}{3}-\frac{1}{3}$
$\Rightarrow \frac{x}{3}=\frac{15-1}{3}$
$\Rightarrow \frac{x}{3}=\frac{14}{3}$

Step 2: Multiply both the sides by 3
$\Rightarrow \frac{x}{3}\times 3=\frac{14}{3}\times 3$
$\Rightarrow x=14$

Hence, the solution of the equation $\frac{x}{3}+\frac{1}{3}=5$ is $x=14.$