CAIE A-Level Mathematics 3.1.1 Modulus equations

Practise solving modulus equations and inequalities by sketching V-shaped graphs, finding intersections and translating bounds.

Exam points

sketch y=|ax+b| with the vertex and axis intercepts positioned correctly
solve modulus inequalities by finding critical values and stating the interval

[Maximum number: 4]

Solve the inequality |2 x+3|>3|x+2|.

Square both sides:
$(2x+3)^2>9(x+2)^2.$
Then
$4x^2+12x+9>9x^2+36x+36,$
so
$5x^2+24x+27<0.$
Factorising,
(5x+9)(x+3)<0.
The critical values are x=-3 and $x=-\frac95$ . The product is negative between them, hence
$-3<x<-\frac95.$

B1 for the non-modular squared inequality or equivalent linear equations. M1 for solving the quadratic/equations. A1 for critical values -3 and $-\frac95$ . A1 for $-3<x<-\frac95$ , with strict inequalities.

Figure for Answer to Question 3.1.1—Modulus equations question 1 — CAIE A-Level Mathematics A2

All question bank results loaded

3.1.1—Modulus equations question 1