Solve x^(2)-3x≥0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

x \in (- \infty, 0] \cup [3, + \infty)

Evaluate

x^{2} - 3 x \geq 0

Rewrite the expression

x^{2} - 3 x = 0

Factor the expression

More Steps

x (x - 3) = 0

When the product of factors equals 0,at least one factor is 0

x = 0 x - 3 = 0

Solve the equation for x

More Steps

x = 0 x = 3

Determine the test intervals using the critical values

x < 0 0 < x < 3 x > 3

Choose a value form each interval

x_{1} = - 1 x_{2} = 2 x_{3} = 4

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} = 2 x_{3} = 4

To determine if 0 < x < 3 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

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x < 0 is the solution 0 < x < 3 is not a solution x_{3} = 4

To determine if x > 3 is the solution to the inequality,test if the chosen value x = 4 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < 3 is not a solution x > 3 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 3 is the solution

Solution

x \in (- \infty, 0] \cup [3, + \infty)

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