Question

Solve each of the following equations. Also, verify the result in each case.

Answer 1

$x-\frac{x}{4}-\frac{1}{2}=3+\frac{x}{4}$
Transposing $\frac{x}{4}$ to LHS and $-\frac{1}{2}$ to RHS, we get
=> $x-\frac{x}{4}-\frac{x}{4}=3+\frac{1}{2}$
=> $\frac{4x-x-x}{4}=\frac{6+1}{2}$
=> $\frac{2x}{4}=\frac{7}{2}$
Multiplying both sides by 4, we get
=> $\frac{2x}{4}\times 4=\frac{7}{2}\times 4$
=> 2x = 14
Dividing both sides by 2, we get
=> $\frac{2x}{2}=\frac{14}{2}$
=> x = 7
Verification:
Substituting x = 7 on both sides, we get

$7-\frac{7}{4}-\frac{1}{2}=3+\frac{7}{4}$
$\frac{28-7-2}{4}=\frac{12+7}{4}$
$\frac{19}{4}=\frac{19}{4}$
LHS = RHS
Hence, verified.