Theory question 102
Inequalities(a) Solve the inequality (2/5)(x − 2) − (1/6)(x + 5) ≤ 0
(b) Given that P = (x2 − y2)/(x2 + xy), (i) express P in its simplest form; (ii) find the value of P if x = −4 and y = −6.
Show the model answer
Model answer
(a) Multiply by 30: 12(x − 2) − 5(x + 5) ≤ 0 → 7x − 49 ≤ 0 → x ≤ 7.
(b)(i) P = (x − y)(x + y)/[x(x + y)] = (x − y)/x.
(ii) P = (−4 − (−6))/(−4) = 2/(−4) = −½.
Explanation
Clear the fractions with the LCM of 5 and 6.