Solve x^2 - 9x < -8

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

1 < x < 8

Alternative Form

x \in (1, 8)

Evaluate

x^{2} - 9 x < - 8

Move the expression to the left side

x^{2} - 9 x - (- 8) < 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x^{2} - 9 x + 8 < 0

Rewrite the expression

x^{2} - 9 x + 8 = 0

Factor the expression

More Steps

(x - 8) (x - 1) = 0

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

x - 8 = 0 x - 1 = 0

Solve the equation for x

More Steps

x = 8 x - 1 = 0

Solve the equation for x

More Steps

x = 8 x = 1

Determine the test intervals using the critical values

x < 1 1 < x < 8 x > 8

Choose a value form each interval

x_{1} = 0 x_{2} = 5 x_{3} = 9

To determine if x < 1 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < 1 is not a solution x_{2} = 5 x_{3} = 9

To determine if 1 < x < 8 is the solution to the inequality,test if the chosen value x = 5 satisfies the initial inequality

More Steps

x < 1 is not a solution 1 < x < 8 is the solution x_{3} = 9

To determine if x > 8 is the solution to the inequality,test if the chosen value x = 9 satisfies the initial inequality

More Steps

x < 1 is not a solution 1 < x < 8 is the solution x > 8 is not a solution

Solution

1 < x < 8

Alternative Form

x \in (1, 8)

Show Solution