Absolute value inequality — Opposite inequality

Question

Solve .

This practice question was inspired by Question 11(f) in the 2022 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Set up the solution: separate the absolute-value statement into its valid algebraic cases.Same critical values and .
State the final answer clearly in the form the question requested.Solution side): or (check signs), more precisely .

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Sign chart with the complementary regions.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.