Solve (x-3)(x-4)>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, 3) \cup (4, + \infty)

Evaluate

(x - 3) (x - 4) > 0

Rewrite the expression

(x - 3) (x - 4) = 0

Separate the equation into 2 possible cases

x - 3 = 0 x - 4 = 0

Solve the equation

More Steps

x = 3 x - 4 = 0

Solve the equation

More Steps

x = 3 x = 4

Determine the test intervals using the critical values

x < 3 3 < x < 4 x > 4

Choose a value form each interval

x_{1} = 2 x_{2} = \frac{7}{2} x_{3} = 5

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

More Steps

x < 3 is the solution x_{2} = \frac{7}{2} x_{3} = 5

To determine if 3 < x < 4 is the solution to the inequality,test if the chosen value x = \frac{7}{2} satisfies the initial inequality

More Steps

x < 3 is the solution 3 < x < 4 is not a solution x_{3} = 5

To determine if x > 4 is the solution to the inequality,test if the chosen value x = 5 satisfies the initial inequality

More Steps

x < 3 is the solution 3 < x < 4 is not a solution x > 4 is the solution

Solution

x \in (- \infty, 3) \cup (4, + \infty)

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