CAIE IGCSE Additional Math 4.2 solve modulus inequalities

Use this modulus-inequalities page to split absolute-value cases or use graphs, then combine intervals into the final solution set.

Exam points

Solve inequalities such as |4x-1|>9 by splitting into algebraic cases.
Use graphs to solve inequalities involving |quadratic| or combined expressions.
Combine the valid intervals and write the final inequality solution clearly.

[Maximum number: 4]

Solve the following inequalities.

|3x-4|<x+2

x * 3
B1
* can be any inequality sign or =.
-3x+4<x+2
or
3x-4>-x-2
M1
$x * \frac{1}{2}$
A1
* can be any inequality sign or =.
$\frac{1}{2}<x<3$
A1
Do not accept $\frac{1}{2}<x,\ x<3$ unless "and" is between the inequalities.
Alternative method:
$9x^2-24x+16 * x^2+4x+4$
(M1) Square both sides; * can be any inequality sign or =.
(2x-1)(x-3) * 0
(M1) * can be any inequality sign or =.
Critical values $\frac{1}{2},\ 3$
(A1)
$\frac{1}{2}<x<3$
(A1)

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4.2. Solve modulus inequalities question 1