Solve a^2 - 12 < 0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for a

- 23 < a < 23

Alternative Form

a \in (- 23, 23)

Evaluate

a^{2} - 12 < 0

Rewrite the expression

a^{2} - 12 = 0

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

a^{2} = 0 + 12

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

a^{2} = 12

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

a = \pm 12

Simplify the expression

More Steps

a = \pm 23

Separate the equation into 2 possible cases

a = 23 a = - 23

Determine the test intervals using the critical values

a < - 23 - 23 < a < 23 a > 23

Choose a value form each interval

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

To determine if a < - 23 is the solution to the inequality,test if the chosen value a = - 4 satisfies the initial inequality

More Steps

a < - 23 is not a solution a_{2} = 0 a_{3} = 4

To determine if - 23 < a < 23 is the solution to the inequality,test if the chosen value a = 0 satisfies the initial inequality

More Steps

a < - 23 is not a solution - 23 < a < 23 is the solution a_{3} = 4

To determine if a > 23 is the solution to the inequality,test if the chosen value a = 4 satisfies the initial inequality

More Steps

a < - 23 is not a solution - 23 < a < 23 is the solution a > 23 is not a solution

Solution

- 23 < a < 23

Alternative Form

a \in (- 23, 23)

Show Solution