Solve (x-2)(x-3)>=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, 2] \cup [3, + \infty)

Evaluate

(x - 2) (x - 3) \geq 0

Rewrite the expression

(x - 2) (x - 3) = 0

Separate the equation into 2 possible cases

x - 2 = 0 x - 3 = 0

Solve the equation

More Steps

x = 2 x - 3 = 0

Solve the equation

More Steps

x = 2 x = 3

Determine the test intervals using the critical values

x < 2 2 < x < 3 x > 3

Choose a value form each interval

x_{1} = 1 x_{2} = \frac{5}{2} x_{3} = 4

To determine if x < 2 is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < 2 is the solution x_{2} = \frac{5}{2} x_{3} = 4

To determine if 2 < x < 3 is the solution to the inequality,test if the chosen value x = \frac{5}{2} satisfies the initial inequality

More Steps

x < 2 is the solution 2 < 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 < 2 is the solution 2 < 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 2 is the solution x \geq 3 is the solution

Solution

x \in (- \infty, 2] \cup [3, + \infty)

Show Solution