Paper 1 · Modulus / inequalities

Solve the inequality $|x-1| < x$ .

x > \tfrac{1}{2}

x < \tfrac{1}{2}

0 < x < 1

x > 1

Explanation: Squaring both sides gives

(x-1)^2<x^2

, i.e.

-2x+1<0

, so

x>\tfrac12

Derived from ZIMSEC Mathematics Paper 1, June 2017, Q1

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