Solve and analyse the following compound inequality.

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Solve and analyse the following compound inequality. (i) Solve 12<3x−46≤54\dfrac{1}{2} < \dfrac{3x-4}{6} \le \dfrac{5}{4}, showing each algebraic step. (ii) At every stage of your working, state whether the inequality signs remain the same or change, and give a brief reason for your answer. (iii) Depict the final solution on a number line with correct open or closed endpoints.

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