Solve 0<(3x^6)^-1<1/3 - ScanMath

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Question

Solve the inequality

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

Evaluate

0 < (3 x^{6})^{- 1} < \frac{1}{3}

Find the domain

More Steps

0 < (3 x^{6})^{- 1} < \frac{1}{3}, x \neq = 0

Separate into two inequalities

{0 < (3 x^{6})^{- 1} (3 x^{6})^{- 1} < \frac{1}{3}

Solve the inequality

More Steps

{x \in R (3 x^{6})^{- 1} < \frac{1}{3}

Solve the inequality

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Evaluate

(3 x^{6})^{- 1} < \frac{1}{3}

Evaluate the power

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\frac{1}{3} x^{- 6} < \frac{1}{3}

Multiply by the reciprocal

\frac{1}{3} x^{- 6} \times 3 < \frac{1}{3} \times 3

Multiply

x^{- 6} < \frac{1}{3} \times 3

Multiply

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x^{- 6} < 1

Move the expression to the left side

x^{- 6} - 1 < 0

Rewrite the expression

\frac{1}{x ^{6}} - 1 < 0

Convert the expressions

\frac{1 - x ^{6}}{x ^{6}} < 0

Separate the inequality into 2 possible cases

{1 - x^{6} > 0 x^{6} < 0 {1 - x^{6} < 0 x^{6} > 0

Solve the inequality

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{- 1 < x < 1 x^{6} < 0 {1 - x^{6} < 0 x^{6} > 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

{- 1 < x < 1 x \in / R {1 - x^{6} < 0 x^{6} > 0

Solve the inequality

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{- 1 < x < 1 x \in / R {x \in (- \infty, - 1) \cup (1, + \infty) x^{6} > 0

Solve the inequality

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

Find the intersection

x \in / R {x \in (- \infty, - 1) \cup (1, + \infty) x \neq = 0

Find the intersection

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

Find the union

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

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

Find the intersection

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

Check if the solution is in the defined range

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

Solution

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

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