Solve x^2\le 16 - ScanMath

Evaluate

x^{2} \leq 16

Move the expression to the left side

x^{2} - 16 \leq 0

Rewrite the expression

x^{2} - 16 = 0

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

x^{2} = 0 + 16

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

x^{2} = 16

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

x = \pm 16

Simplify the expression

More Steps

x = \pm 4

Separate the equation into 2 possible cases

x = 4 x = - 4

Determine the test intervals using the critical values

x < - 4 - 4 < x < 4 x > 4

Choose a value form each interval

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

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

More Steps

x < - 4 is not a solution x_{2} = 0 x_{3} = 5

To determine if - 4 < x < 4 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 4 is not a solution - 4 < x < 4 is the solution x_{3} = 5

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

More Steps

x < - 4 is not a solution - 4 < x < 4 is the solution x > 4 is not a solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

- 4 \leq x \leq 4 is the solution

Solution

- 4 \leq x \leq 4

Alternative Form

x \in [- 4, 4]

X^2\le 16