Solve (x - 2)(x 1)(x^5) ≥ 0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

x \in [2, + \infty) \cup {0}

Evaluate

(x - 2) (x \times 1) x^{5} \geq 0

Remove the parentheses

(x - 2) x \times 1 \times x^{5} \geq 0

Multiply the terms

More Steps

x^{6} (x - 2) \geq 0

Rewrite the expression

x^{6} (x - 2) = 0

Separate the equation into 2 possible cases

x^{6} = 0 x - 2 = 0

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

x = 0 x - 2 = 0

Solve the equation

More Steps

x = 0 x = 2

Determine the test intervals using the critical values

x < 0 0 < x < 2 x > 2

Choose a value form each interval

x_{1} = - 1 x_{2} = 1 x_{3} = 3

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 x_{3} = 3

To determine if 0 < x < 2 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 0 < x < 2 is not a solution x_{3} = 3

To determine if x > 2 is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < 0 is not a solution 0 < x < 2 is not a solution x > 2 is the solution

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

x \geq 2 is the solution x = 0

Solution

x \in [2, + \infty) \cup {0}

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