Solve root()(2x^4)> (2x 1)/2 - ScanMath

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Type your math problem... root()(2x^4)> (2x 1)/2

Question

Solve the inequality

x \in (- \infty, 0) \cup (\frac{2}{2}, + \infty)

Evaluate

2 x^{4} > \frac{2 x \times 1}{2}

Reduce the fraction

More Steps

2 x^{4} > x

Separate the inequality into 2 possible cases

2 x^{4} > x, x \geq 0 2 x^{4} > x, x < 0

Solve the inequality

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Solve the inequality

2 x^{4} > x

Square both sides of the inequality

2 x^{4} > x^{2}

Move the expression to the left side

2 x^{4} - x^{2} > 0

Factor the expression

x^{2} (2 x^{2} - 1) > 0

Separate the inequality into 2 possible cases

{x^{2} > 0 2 x^{2} - 1 > 0 {x^{2} < 0 2 x^{2} - 1 < 0

Solve the inequality

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{x \neq = 0 2 x^{2} - 1 > 0 {x^{2} < 0 2 x^{2} - 1 < 0

Solve the inequality

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

Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is false for any value of x

{x \neq = 0 x \in (- \infty, - \frac{2}{2}) \cup (\frac{2}{2}, + \infty) {x \in / R 2 x^{2} - 1 < 0

Solve the inequality

More Steps

{x \neq = 0 x \in (- \infty, - \frac{2}{2}) \cup (\frac{2}{2}, + \infty) {x \in / R - \frac{2}{2} < x < \frac{2}{2}

Find the intersection

x \in (- \infty, - \frac{2}{2}) \cup (\frac{2}{2}, + \infty) {x \in / R - \frac{2}{2} < x < \frac{2}{2}

Find the intersection

x \in (- \infty, - \frac{2}{2}) \cup (\frac{2}{2}, + \infty) x \in / R

Find the union

x \in (- \infty, - \frac{2}{2}) \cup (\frac{2}{2}, + \infty)

x \in (- \infty, - \frac{2}{2}) \cup (\frac{2}{2}, + \infty), x \geq 0 2 x^{4} > x, x < 0

Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is true for any value of x

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

Find the intersection

x > \frac{2}{2} x \in R, x < 0

Find the intersection

x > \frac{2}{2} x < 0

Solution

x \in (- \infty, 0) \cup (\frac{2}{2}, + \infty)

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