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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 $10$.
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