Solve x/(2x^5) <7x - ScanMath

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Type your math problem... x/(2x^5) <7x

Question

Solve the inequality

x > \frac{5 38416}{14}

Alternative Form

x \in (\frac{5 38416}{14}, + \infty)

Evaluate

\frac{x}{2 x ^{5}} < 7 x

Find the domain

More Steps

\frac{x}{2 x ^{5}} < 7 x, x \neq = 0

Divide the terms

More Steps

\frac{1}{2 x ^{4}} < 7 x

Move the expression to the left side

\frac{1}{2 x ^{4}} - 7 x < 0

Subtract the terms

More Steps

\frac{1 - 14 x ^{5}}{2 x ^{4}} < 0

Separate the inequality into 2 possible cases

{1 - 14 x^{5} > 0 2 x^{4} < 0 {1 - 14 x^{5} < 0 2 x^{4} > 0

Solve the inequality

More Steps

{x < \frac{5 38416}{14} 2 x^{4} < 0 {1 - 14 x^{5} < 0 2 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 < \frac{5 38416}{14} x \in / R {1 - 14 x^{5} < 0 2 x^{4} > 0

Solve the inequality

More Steps

{x < \frac{5 38416}{14} x \in / R {x > \frac{5 38416}{14} 2 x^{4} > 0

Solve the inequality

More Steps

{x < \frac{5 38416}{14} x \in / R {x > \frac{5 38416}{14} x \neq = 0

Find the intersection

x \in / R {x > \frac{5 38416}{14} x \neq = 0

Find the intersection

x \in / R x > \frac{5 38416}{14}

Find the union

x > \frac{5 38416}{14}

Check if the solution is in the defined range

x > \frac{5 38416}{14}, x \neq = 0

Solution

x > \frac{5 38416}{14}

Alternative Form

x \in (\frac{5 38416}{14}, + \infty)

Show Solution