Question

Solve the following equation and check your results:
$2y+\frac{5}{3}=\frac{26}{3}-y$

Answer 1

Transpose $\frac{5}{3}$ to RHS and $y$ to LHS

$2y+y=\frac{26}{3}-\frac{5}{3}$

$\Rightarrow 3y=\frac{26-5}{3}$

$\Rightarrow 3y=\frac{21}{3}$

$\Rightarrow 3y=7$

Divide both sides by $3$
$y=\frac{7}{3}$

LHS $\Rightarrow 2y+\frac{5}{3}=\frac{2\times 7}{3}+\frac{5}{3}=\frac{14}{3}+\frac{5}{3}=\frac{19}{3}$

RHS $\Rightarrow \frac{26}{3}-y=\frac{26}{3}-\frac{7}{3}=\frac{26-7}{3}=\frac{19}{3}$

LHS $=$ RHS
Hence proved.