Solve [x]^2 -3[x] 2 >= 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 [6, + \infty)

Evaluate

x^{2} - 3 x \times 2 \geq 0

Multiply the terms

x^{2} - 6 x \geq 0

Rewrite the expression

x^{2} - 6 x = 0

Factor the expression

More Steps

x (x - 6) = 0

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

x = 0 x - 6 = 0

Solve the equation for x

More Steps

x = 0 x = 6

Determine the test intervals using the critical values

x < 0 0 < x < 6 x > 6

Choose a value form each interval

x_{1} = - 1 x_{2} = 3 x_{3} = 7

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} = 7

To determine if 0 < x < 6 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 < 6 is not a solution x_{3} = 7

To determine if x > 6 is the solution to the inequality,test if the chosen value x = 7 satisfies the initial inequality

More Steps

x < 0 is the solution 0 < x < 6 is not a solution x > 6 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 6 is the solution

Solution

x \in (- \infty, 0] \cup [6, + \infty)

Show Solution