Solve (x 1)x^2(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 (- \infty, 0] \cup [5, + \infty)

Evaluate

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

Remove the parentheses

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

Multiply the terms

More Steps

x^{3} (x - 5) \geq 0

Rewrite the expression

x^{3} (x - 5) = 0

Separate the equation into 2 possible cases

x^{3} = 0 x - 5 = 0

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

x = 0 x - 5 = 0

Solve the equation

More Steps

x = 0 x = 5

Determine the test intervals using the critical values

x < 0 0 < x < 5 x > 5

Choose a value form each interval

x_{1} = - 1 x_{2} = 3 x_{3} = 6

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} = 3 x_{3} = 6

To determine if 0 < x < 5 is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < 5 is not a solution x_{3} = 6

To determine if x > 5 is the solution to the inequality,test if the chosen value x = 6 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < 5 is not a solution x > 5 is the solution

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

x \leq 0 is the solution x \geq 5 is the solution

Solution

x \in (- \infty, 0] \cup [5, + \infty)

Show Solution