Solve (x^2-5x^6)/(|x| 7) <0

Evaluate

\frac{x ^{2} - 5 x ^{6}}{∣ x ∣ \times 7} < 0

Find the domain

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\frac{x ^{2} - 5 x ^{6}}{∣ x ∣ \times 7} < 0, x \neq = 0

Multiply the terms

\frac{x ^{2} - 5 x ^{6}}{7 ∣ x ∣} < 0

Separate the inequality into 2 possible cases

{x^{2} - 5 x^{6} > 0 7 ∣ x ∣ < 0 {x^{2} - 5 x^{6} < 0 7 ∣ x ∣ > 0

Solve the inequality

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Evaluate

x^{2} - 5 x^{6} > 0

Factor the expression

x^{2} (1 - 5 x^{4}) > 0

Separate the inequality into 2 possible cases

{x^{2} > 0 1 - 5 x^{4} > 0 {x^{2} < 0 1 - 5 x^{4} < 0

Solve the inequality

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{x \neq = 0 1 - 5 x^{4} > 0 {x^{2} < 0 1 - 5 x^{4} < 0

Solve the inequality

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{x \neq = 0 - \frac{4 125}{5} < x < \frac{4 125}{5} {x^{2} < 0 1 - 5 x^{4} < 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 - \frac{4 125}{5} < x < \frac{4 125}{5} {x \in / R 1 - 5 x^{4} < 0

Solve the inequality

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{x \neq = 0 - \frac{4 125}{5} < x < \frac{4 125}{5} {x \in / R x \in (- \infty, - \frac{4 125}{5}) \cup (\frac{4 125}{5}, + \infty)

Find the intersection

x \in (- \frac{4 125}{5}, 0) \cup (0, \frac{4 125}{5}) {x \in / R x \in (- \infty, - \frac{4 125}{5}) \cup (\frac{4 125}{5}, + \infty)

Find the intersection

x \in (- \frac{4 125}{5}, 0) \cup (0, \frac{4 125}{5}) x \in / R

Find the union

x \in (- \frac{4 125}{5}, 0) \cup (0, \frac{4 125}{5})

{x \in (- \frac{4 125}{5}, 0) \cup (0, \frac{4 125}{5}) 7 ∣ x ∣ < 0 {x^{2} - 5 x^{6} < 0 7 ∣ x ∣ > 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 \in (- \frac{4 125}{5}, 0) \cup (0, \frac{4 125}{5}) x \in / R {x^{2} - 5 x^{6} < 0 7 ∣ x ∣ > 0

Solve the inequality

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Evaluate

x^{2} - 5 x^{6} < 0

Factor the expression

x^{2} (1 - 5 x^{4}) < 0

Separate the inequality into 2 possible cases

{x^{2} > 0 1 - 5 x^{4} < 0 {x^{2} < 0 1 - 5 x^{4} > 0

Solve the inequality

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{x \neq = 0 1 - 5 x^{4} < 0 {x^{2} < 0 1 - 5 x^{4} > 0

Solve the inequality

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{x \neq = 0 x \in (- \infty, - \frac{4 125}{5}) \cup (\frac{4 125}{5}, + \infty) {x^{2} < 0 1 - 5 x^{4} > 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{4 125}{5}) \cup (\frac{4 125}{5}, + \infty) {x \in / R 1 - 5 x^{4} > 0

Solve the inequality

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{x \neq = 0 x \in (- \infty, - \frac{4 125}{5}) \cup (\frac{4 125}{5}, + \infty) {x \in / R - \frac{4 125}{5} < x < \frac{4 125}{5}

Find the intersection

x \in (- \infty, - \frac{4 125}{5}) \cup (\frac{4 125}{5}, + \infty) {x \in / R - \frac{4 125}{5} < x < \frac{4 125}{5}

Find the intersection

x \in (- \infty, - \frac{4 125}{5}) \cup (\frac{4 125}{5}, + \infty) x \in / R

Find the union

x \in (- \infty, - \frac{4 125}{5}) \cup (\frac{4 125}{5}, + \infty)

{x \in (- \frac{4 125}{5}, 0) \cup (0, \frac{4 125}{5}) x \in / R {x \in (- \infty, - \frac{4 125}{5}) \cup (\frac{4 125}{5}, + \infty) 7 ∣ x ∣ > 0

Solve the inequality

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{x \in (- \frac{4 125}{5}, 0) \cup (0, \frac{4 125}{5}) x \in / R {x \in (- \infty, - \frac{4 125}{5}) \cup (\frac{4 125}{5}, + \infty) x \neq = 0

Find the intersection

x \in / R {x \in (- \infty, - \frac{4 125}{5}) \cup (\frac{4 125}{5}, + \infty) x \neq = 0

Find the intersection

x \in / R x \in (- \infty, - \frac{4 125}{5}) \cup (\frac{4 125}{5}, + \infty)

Find the union

x \in (- \infty, - \frac{4 125}{5}) \cup (\frac{4 125}{5}, + \infty)

Check if the solution is in the defined range

x \in (- \infty, - \frac{4 125}{5}) \cup (\frac{4 125}{5}, + \infty), x \neq = 0

Solution

x \in (- \infty, - \frac{4 125}{5}) \cup (\frac{4 125}{5}, + \infty)