Question

Solve each of the following equations. Also, verify the result in each case.
$\frac{x}{2}+\frac{3}{2}=\frac{2x}{5}-1$

Answer 1

$\frac{x}{2}+\frac{3}{2}=\frac{2x}{5}-1$
Transposing $\frac{2x}{5}$ to LHS and $\frac{3}{2}$ to RHS, we get
=> $\frac{x}{2}-\frac{2x}{5}=-1-\frac{3}{2}$

=> $\frac{5x-4x}{10}=\frac{-2-3}{2}$
=> $\frac{x}{10}=\frac{-5}{2}$
Multiplying both sides by 10, we get
=> $\frac{x}{10}\times 10=\frac{-5}{2}\times 10$
=> x = $-25$
Verification:
Substituting x = $-25$ in the given equation, we get
$\frac{-25}{2}+\frac{3}{2}=\frac{2\times \left(-25\right)}{5}-1$
$\frac{-22}{2}=-10-1$
$-11=-11$
LHS = RHS
Hence, verified.