Solve x-1 x≤2x^5

Evaluate

x - 1 \times x \leq 2 x^{5}

Simplify

More Steps

0 \leq 2 x^{5}

Move the expression to the left side

0 - 2 x^{5} \leq 0

Removing 0 doesn't change the value,so remove it from the expression

- 2 x^{5} \leq 0

Rewrite the expression

- 2 x^{5} = 0

Change the signs on both sides of the equation

2 x^{5} = 0

Rewrite the expression

x^{5} = 0

The only way a power can be 0 is when the base equals 0

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 not a 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 not a solution x > 0 is the solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

x \geq 0 is the solution

Solution

x \geq 0

Alternative Form

x \in [0, + \infty)

Solve the inequality