Theory question 102
Inequalities(a) Solve the inequality: 4 + ¾(x + 2) ≤ ⅜x + 1.
(b) The diagram shows a rectangle PQRS from which a square of side x cm has been cut. If the area of the shaded portion is 484 cm2, find the values of x.
Show the model answer
Model answer
(a) Multiply through by 8: 32 + 6(x + 2) ≤ 3x + 8
6x + 44 ≤ 3x + 8 → 3x ≤ −36 → x ≤ −12
(b) The rectangle is 20 cm high and (10 + x + 10) = (20 + x) cm long.
Shaded area = 20(20 + x) − x² = 484
400 + 20x − x² = 484 → x² − 20x + 84 = 0 → (x − 6)(x − 14) = 0
x = 6 cm or x = 14 cm
Explanation
In (b), the length of the rectangle includes the cut-out width x.