CAIE IGCSE Additional Math 4.2 Solve Modulus Inequalities Questions

Practise Cambridge IGCSE Additional Mathematics by solving absolute-value inequalities and expressing complete solution intervals.

Exam points

Solve absolute-value inequalities by considering sign cases and interval boundaries.
Use graphical or algebraic methods to compare absolute-value expressions.
State the complete solution set with correct inequality notation and endpoint inclusion.

[Maximum number: 3]

Figure for Question CAIE IGCSE Additional Math 4.2 Solve Modulus Inequalities Questions question 1 — CAIE IGCSE Additional Math

The diagram shows the graph of y=|3x+3|.
Use a graphical method to solve the inequality $|3x+3| \geqslant |x-2|$ .

Correct graph of y=|x-2| and $x \leqslant -2.5,\ x \geqslant -0.25$
B1 for correct graph of y=|x-2|.
B1 for $x \leqslant -2.5$ or $x \geqslant -0.25$ .
B1 STRICT FT for their critical values from the two intersections of their straight-line section of graph, providing it has negative gradient.

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CAIE IGCSE Additional Math 4.2 Solve Modulus Inequalities Questions question 1