WAEC 2016 · Paper 2 · Q2

(a)
Solve: $7(x + 4) - \frac23(x - 6) \le 2[x - 3(x + 5)]$ .
Show the answer
$x \le -6$
(b)
A transport company has a total of 20 vehicles made up of tricycles and taxicabs. Each tricycle carries 2 passengers while each taxicab carries 4 passengers. If the 20 vehicles carry a total of 66 passengers at a time, how many tricycles does the company have?

Worked solution (try it first)

Simplify the right side first: $2[x - 3(x + 5)] = 2[x - 3x - 15]$
$= 2(-2x - 15)$
$= -4x - 30$ .
Multiply every term by 3 to clear the fraction: $21(x + 4) - 2(x - 6) \le 3(-4x - 30)$ .
Expand: $21x + 84 - 2x + 12 \le -12x - 90$ .
So $19x + 96 \le -12x - 90$ .
Collect terms: $31x \le -186$ .
Divide by 31 (positive, so the sign stays the same): $x \le -6$ .