JAMB 2002 · UME · Q41

Find the range of values of $x$ for which $\dfrac{x + 2}{4} - \dfrac{2x - 3}{3} < 4$ .

Worked solution (try it first)

Multiply every term by 12, the LCM of 4 and 3: $3(x + 2) - 4(2x - 3) < 48$ .
Expand, taking care with the minus: $3x + 6 - 8x + 12 < 48$ , so $-5x + 18 < 48$ .
Subtract 18 from both sides: $-5x < 30$ .
Divide by $-5$ and reverse the sign: $x > -6$ , option C.