Solve x^2-7x+10>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 (5, + \infty)

Evaluate

x^{2} - 7 x + 10 > 0

Rewrite the expression

x^{2} - 7 x + 10 = 0

Factor the expression

More Steps

(x - 5) (x - 2) = 0

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

x - 5 = 0 x - 2 = 0

Solve the equation for x

More Steps

x = 5 x - 2 = 0

Solve the equation for x

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x = 5 x = 2

Determine the test intervals using the critical values

x < 2 2 < x < 5 x > 5

Choose a value form each interval

x_{1} = 1 x_{2} = 4 x_{3} = 6

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} = 4 x_{3} = 6

To determine if 2 < x < 5 is the solution to the inequality,test if the chosen value x = 4 satisfies the initial inequality

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x < 2 is the solution 2 < 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 < 2 is the solution 2 < x < 5 is not a solution x > 5 is the solution

Solution

x \in (- \infty, 2) \cup (5, + \infty)

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