Solve 20>z^2 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for z

- 25 < z < 25

Alternative Form

z \in (- 25, 25)

Evaluate

20 > z^{2}

Move the expression to the left side

20 - z^{2} > 0

Rewrite the expression

20 - z^{2} = 0

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

- z^{2} = 0 - 20

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

- z^{2} = - 20

Change the signs on both sides of the equation

z^{2} = 20

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

z = \pm 20

Simplify the expression

More Steps

z = \pm 25

Separate the equation into 2 possible cases

z = 25 z = - 25

Determine the test intervals using the critical values

z < - 25 - 25 < z < 25 z > 25

Choose a value form each interval

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

To determine if z < - 25 is the solution to the inequality,test if the chosen value z = - 5 satisfies the initial inequality

More Steps

z < - 25 is not a solution z_{2} = 0 z_{3} = 5

To determine if - 25 < z < 25 is the solution to the inequality,test if the chosen value z = 0 satisfies the initial inequality

More Steps

z < - 25 is not a solution - 25 < z < 25 is the solution z_{3} = 5

To determine if z > 25 is the solution to the inequality,test if the chosen value z = 5 satisfies the initial inequality

More Steps

z < - 25 is not a solution - 25 < z < 25 is the solution z > 25 is not a solution

Solution

- 25 < z < 25

Alternative Form

z \in (- 25, 25)

Show Solution