Solve x^2<19 - ScanMath

Evaluate

x^{2} < 19

Move the expression to the left side

x^{2} - 19 < 0

Rewrite the expression

x^{2} - 19 = 0

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

x^{2} = 0 + 19

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

x^{2} = 19

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

x = \pm 19

Separate the equation into 2 possible cases

x = 19 x = - 19

Determine the test intervals using the critical values

x < - 19 - 19 < x < 19 x > 19

Choose a value form each interval

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

To determine if x < - 19 is the solution to the inequality,test if the chosen value x = - 5 satisfies the initial inequality

More Steps

x < - 19 is not a solution x_{2} = 0 x_{3} = 5

To determine if - 19 < x < 19 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 19 is not a solution - 19 < x < 19 is the solution x_{3} = 5

To determine if x > 19 is the solution to the inequality,test if the chosen value x = 5 satisfies the initial inequality

More Steps

x < - 19 is not a solution - 19 < x < 19 is the solution x > 19 is not a solution

Solution

- 19 < x < 19

Alternative Form

x \in (- 19, 19)

Solve the inequality