Solve -x^5> x/4 - ScanMath

Evaluate

- x^{5} > \frac{x}{4}

Multiply both sides of the inequality by 4

- x^{5} \times 4 > \frac{x}{4} \times 4

Multiply the terms

- 4 x^{5} > \frac{x}{4} \times 4

Multiply the terms

- 4 x^{5} > x

Move the expression to the left side

- 4 x^{5} - x > 0

Rewrite the expression

- 4 x^{5} - x = 0

Factor the expression

- x (4 x^{4} + 1) = 0

Divide both sides

x (4 x^{4} + 1) = 0

Separate the equation into 2 possible cases

x = 0 4 x^{4} + 1 = 0

Solve the equation

More Steps

x = 0 x \in / R

Find the union

x = 0

Determine the test intervals using the critical values

x < 0 x > 0

Choose a value form each interval

x_{1} = - 1 x_{2} = 1

To determine if x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < 0 is the solution x_{2} = 1

To determine if x > 0 is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < 0 is the solution x > 0 is not a solution

Solution

x < 0

Alternative Form

x \in (- \infty, 0)

Solve the inequality