Question 96

Solve the inequality.
$$\frac{x + 1}{2x - 1} > 1$$

Solution

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In this question, we need to assume two cases for the sign of the denominator because of the inequality.

Case 1: 2x-1 > 0, or x> $$\frac{\ 1}{2}$$

This makes x+1 > 2x-1, or x<2

Hence, the range is $$\frac{\ 1}{2}$$ < x < 2

Case 2: 2x-1 < 0, or x < $$\frac{\ 1}{2}$$

This makes x+1 < 2x-1, or x > $$\frac{\ 1}{2}$$

This case is inconsistent in nature. Hence, the answer is $$\frac{\ 1}{2}$$ < x < 2

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