Solve |x| < 42|x| 53|x| 1

Question

Solve the inequality

x \in (- \infty, - \frac{1}{2226}) \cup (\frac{1}{2226}, + \infty)

Evaluate

∣ x ∣ < 42 ∣ x ∣ \times 53 ∣ x ∣ \times 1

Multiply the terms

More Steps

∣ x ∣ < 2226 x^{2}

Rearrange the terms

∣ x ∣ - 2226 x^{2} < 0

Separate the inequality into 2 possible cases

x - 2226 x^{2} < 0, x \geq 0 - x - 2226 x^{2} < 0, x < 0

Evaluate

More Steps

x \in (- \infty, 0) \cup (\frac{1}{2226}, + \infty), x \geq 0 - x - 2226 x^{2} < 0, x < 0

Evaluate

More Steps

x \in (- \infty, 0) \cup (\frac{1}{2226}, + \infty), x \geq 0 x \in (- \infty, - \frac{1}{2226}) \cup (0, + \infty), x < 0

Find the intersection

x > \frac{1}{2226} x \in (- \infty, - \frac{1}{2226}) \cup (0, + \infty), x < 0

Find the intersection

x > \frac{1}{2226} x < - \frac{1}{2226}

Solution

x \in (- \infty, - \frac{1}{2226}) \cup (\frac{1}{2226}, + \infty)

Show Solution