Solve the following equations and check your results.
$ \frac{2 x}{3}+1=\frac{7 x}{15}+3 $.

Given:

\( \frac{2 x}{3}+1=\frac{7 x}{15}+3 \)

To do:
 We have to solve the given equation and check the result.

Solution:

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

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

$\frac{5(2 x)-7x}{15}=2$           (LCM of 3 and 15 is 15)

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

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

$3x=15(2)$

$3x=30$

$x=\frac{30}{3}$

$x=10$

Substituting the value of $x$ in LHS, we get,

$\frac{2 x}{3}+1=\frac{2 (10)}{3}+1$

$=\frac{20}{3}+1$

$=\frac{20+1(3)}{3}$

$=\frac{20+3}{3}$

$=\frac{23}{3}$

Substituting the value of $x$ in RHS, we get,

$\frac{7 x}{15}+3=\frac{7 (10)}{15}+3$

$=\frac{70}{15}+3$

$=\frac{70+3(15)}{15}$

$=\frac{70+45}{15}$

$=\frac{115}{15}$

$=\frac{23}{3}$

LHS $=$ RHS

The value of $x$ is $10$.