Solve |x^2| > |x^5|

Question

Solve the inequality

x \in (- 1, 0) \cup (0, 1)

Evaluate

x^{2} > x^{5}

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

x^{2} > x^{5}

Swap the sides

x^{5} < x^{2}

Rearrange the terms

x^{5} - x^{2} < 0

Separate the inequality into 2 possible cases

x^{5} - x^{2} < 0, x^{5} \geq 0 - x^{5} - x^{2} < 0, x^{5} < 0

Evaluate

More Steps

x \in (- \infty, 0) \cup (0, 1), x^{5} \geq 0 - x^{5} - x^{2} < 0, x^{5} < 0

The only way a base raised to an odd power can be greater than or equal to 0 is if the base is greater than or equal to 0

x \in (- \infty, 0) \cup (0, 1), x \geq 0 - x^{5} - x^{2} < 0, x^{5} < 0

Evaluate

More Steps

x \in (- \infty, 0) \cup (0, 1), x \geq 0 x \in (- 1, 0) \cup (0, + \infty), x^{5} < 0

The only way a base raised to an odd power can be less than 0 is if the base is less than 0

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

Find the intersection

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

Find the intersection

0 < x < 1 - 1 < x < 0

Solution

x \in (- 1, 0) \cup (0, 1)

Show Solution