Question

Solve the following equation and check your result:
$\frac{2x}{3}+1=\frac{7x}{15}+3$

Answer 1

Transpose $\frac{7x}{15}$ to LHS and $1$ to RHS

$\Rightarrow \frac{2x}{3}-\frac{7x}{15}=3-1$

$\Rightarrow \frac{10x-7x}{15}=2$

$\Rightarrow \frac{3x}{15}=2$

$\Rightarrow \frac{x}{5}=2$

Multiply both sides by $5$,

$\Rightarrow x=10$
LHS:

$\Rightarrow \frac{2x}{3}+1=\frac{2}{3}\times 10+1=\frac{23}{3}$

RHS:

$\Rightarrow \frac{7x}{15}+3=\frac{7}{15}\times 10+3=\frac{14}{3}+3=\frac{14+9}{3}=\frac{23}{3}$

LHS $=$ RHS
Hence proved