Solve |4k^2| > 8 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for k

k \in (- \infty, - 2) \cup (2, + \infty)

Evaluate

4 k^{2} > 8

Calculate the absolute value

More Steps

4 k^{2} > 8

Move the expression to the left side

4 k^{2} - 8 > 0

Rewrite the expression

4 k^{2} - 8 = 0

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

4 k^{2} = 0 + 8

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

4 k^{2} = 8

Divide both sides

\frac{4 k ^{2}}{4} = \frac{8}{4}

Divide the numbers

k^{2} = \frac{8}{4}

Divide the numbers

More Steps

k^{2} = 2

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

k = \pm 2

Separate the equation into 2 possible cases

k = 2 k = - 2

Determine the test intervals using the critical values

k < - 2 - 2 < k < 2 k > 2

Choose a value form each interval

k_{1} = - 2 k_{2} = 0 k_{3} = 2

To determine if k < - 2 is the solution to the inequality,test if the chosen value k = - 2 satisfies the initial inequality

More Steps

k < - 2 is the solution k_{2} = 0 k_{3} = 2

To determine if - 2 < k < 2 is the solution to the inequality,test if the chosen value k = 0 satisfies the initial inequality

More Steps

k < - 2 is the solution - 2 < k < 2 is not a solution k_{3} = 2

To determine if k > 2 is the solution to the inequality,test if the chosen value k = 2 satisfies the initial inequality

More Steps

k < - 2 is the solution - 2 < k < 2 is not a solution k > 2 is the solution

Solution

k \in (- \infty, - 2) \cup (2, + \infty)

Show Solution