CAT 2025 Inequalities Question (Hard)

Question

The set of all real values of for which , is

Accepted Answer

We are asked to solve x 2 - x 9 x 0 Split into two cases based on the absolute value. Case 1 x 9 ge 0 Rightarrow x ge -9 x 9 x 9 Inequality becomes x 2 - x 9 x 0 implies x 2 - 9 0 implies x-3 x 3 0 So x3. Combined with x ge -9, we get x in -9,-3 cup 3, infty Case 2 x 9 0 implies x 2 2x 9 0 The quadr

CAT 2025

Quantitative

Inequalities

Hard

The set of all real values of $x$ for which $\left(x^2 - |x+9| + x\right) > 0$ , is

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