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Paper 2 · Functions and Graphs

Solve the inequality 2x−3<3x−4\dfrac2{x-3}<\dfrac3{x-4}.

Model answer

1<x<3 or x>4

Also accepted: 1 to 3, or greater than 4, (1,3) union (4,infinity)

Explanation: Rearranging gives 1−x(x−3)(x−4)<0\dfrac{1-x}{(x-3)(x-4)}<0; a sign table with critical values x=1,3,4x=1,3,4 gives the solution 1<x<31<x<3 or x>4x>4.

Derived from ZIMSEC Pure Mathematics Paper 2, November 2025, Q6

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