Question

Solve the linear equation:

$\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$

• A. $x=3.2$
• B. $x=9$
• C. $x=2.7$
• D. $x=5$

Answer 1

The correct option is C $x=2.7$

Given, $\frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4}$

The denominators on two sides are $2,3,4$ and $5$.

Their LCM is $60$.

Multiplying both sides by $60$, we get

$60\times (\frac{x}{2}-\frac{1}{5})=60\times (\frac{x}{3}+\frac{1}{4})$

$\Rightarrow 60\times \frac{x}{2}-60\times \frac{1}{5}=60\times \frac{x}{3}+60\times \frac{1}{4}$

$\Rightarrow 30x-12=20x+15$

$\Rightarrow 30x-20x=15+12$

$\Rightarrow 10x=27$

$\Rightarrow x=\frac{27}{10}$

$\Rightarrow x=2.7$