Solve m^2-9 >0 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for m

m \in (- \infty, - 3) \cup (3, + \infty)

Evaluate

m^{2} - 9 > 0

Rewrite the expression

m^{2} - 9 = 0

Move the constant to the right-hand side and change its sign

m^{2} = 0 + 9

Removing 0 doesn't change the value,so remove it from the expression

m^{2} = 9

Take the root of both sides of the equation and remember to use both positive and negative roots

m = \pm 9

Simplify the expression

More Steps

m = \pm 3

Separate the equation into 2 possible cases

m = 3 m = - 3

Determine the test intervals using the critical values

m < - 3 - 3 < m < 3 m > 3

Choose a value form each interval

m_{1} = - 4 m_{2} = 0 m_{3} = 4

To determine if m < - 3 is the solution to the inequality,test if the chosen value m = - 4 satisfies the initial inequality

More Steps

m < - 3 is the solution m_{2} = 0 m_{3} = 4

To determine if - 3 < m < 3 is the solution to the inequality,test if the chosen value m = 0 satisfies the initial inequality

More Steps

m < - 3 is the solution - 3 < m < 3 is not a solution m_{3} = 4

To determine if m > 3 is the solution to the inequality,test if the chosen value m = 4 satisfies the initial inequality

More Steps

m < - 3 is the solution - 3 < m < 3 is not a solution m > 3 is the solution

Solution

m \in (- \infty, - 3) \cup (3, + \infty)

Show Solution