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

$x$

Prepare for WAT & GD Like Never Before!

Practice

Features

Support

CAT 2025

Quantitative

Inequalities

Hard

The set of all real values of xxx for which (x2−∣x+9∣+x)>0\left(x^2 - |x+9| + x\right) > 0(x2−∣x+9∣+x)>0, is

Prepare for WAT & GD Like Never Before!

$x$