Solve |x^2|>|x 1|

Evaluate

x^{2} > ∣ x \times 1 ∣

When the expression in absolute value bars is not negative, remove the bars

x^{2} > ∣ x \times 1 ∣

Any expression multiplied by 1 remains the same

x^{2} > ∣ x ∣

Swap the sides

∣ x ∣ < x^{2}

Rearrange the terms

∣ x ∣ - x^{2} < 0

Separate the inequality into 2 possible cases

x - x^{2} < 0, x \geq 0 - x - x^{2} < 0, x < 0

Evaluate

More Steps

x \in (- \infty, 0) \cup (1, + \infty), x \geq 0 - x - x^{2} < 0, x < 0

Evaluate

More Steps

x \in (- \infty, 0) \cup (1, + \infty), x \geq 0 x \in (- \infty, - 1) \cup (0, + \infty), x < 0

Find the intersection

x > 1 x \in (- \infty, - 1) \cup (0, + \infty), x < 0

Find the intersection

x > 1 x < - 1

Solution

x \in (- \infty, - 1) \cup (1, + \infty)

Solve the inequality