Variation 3 · answer guide
Absolute value inequality — Squared-denominator method
Question
Solve by multiplying through by .
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.
Step by step
- Set up the solution: separate the absolute-value statement into its valid algebraic cases. for .
- State the final answer clearly in the form the question requested.Bring to after factoring; solution .
Common mistake: changing so many features that the new example no longer tests the same mathematical idea.
Verification: Squaring the denominator preserves inequality direction.
Any mark labels are a TestMum study aid, not an official NESA marking allocation.
← Back to 2022 HSC Extension 1 paper Question 11(f)