Solve 4|2x^2|-2≥6

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for x

x \in (- \infty, - 1] \cup [1, + \infty)

Evaluate

4 2 x^{2} - 2 \geq 6

Simplify

More Steps

8 x^{2} - 2 \geq 6

Move the expression to the left side

8 x^{2} - 2 - 6 \geq 0

Subtract the numbers

8 x^{2} - 8 \geq 0

Rewrite the expression

8 x^{2} - 8 = 0

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

8 x^{2} = 0 + 8

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

8 x^{2} = 8

Divide both sides

\frac{8 x ^{2}}{8} = \frac{8}{8}

Divide the numbers

x^{2} = \frac{8}{8}

Divide the numbers

More Steps

x^{2} = 1

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

x = \pm 1

Simplify the expression

x = \pm 1

Separate the equation into 2 possible cases

x = 1 x = - 1

Determine the test intervals using the critical values

x < - 1 - 1 < x < 1 x > 1

Choose a value form each interval

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

To determine if x < - 1 is the solution to the inequality,test if the chosen value x = - 2 satisfies the initial inequality

More Steps

x < - 1 is the solution x_{2} = 0 x_{3} = 2

To determine if - 1 < x < 1 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 1 is the solution - 1 < x < 1 is not a solution x_{3} = 2

To determine if x > 1 is the solution to the inequality,test if the chosen value x = 2 satisfies the initial inequality

More Steps

x < - 1 is the solution - 1 < x < 1 is not a solution x > 1 is the solution

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

x \leq - 1 is the solution x \geq 1 is the solution

Solution

x \in (- \infty, - 1] \cup [1, + \infty)

Show Solution