Solve 4x^2-7<x^2-1

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

- 2 < x < 2

Alternative Form

x \in (- 2, 2)

Evaluate

4 x^{2} - 7 < x^{2} - 1

Move the expression to the left side

4 x^{2} - 7 - (x^{2} - 1) < 0

Subtract the terms

More Steps

3 x^{2} - 6 < 0

Rewrite the expression

3 x^{2} - 6 = 0

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

3 x^{2} = 0 + 6

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

3 x^{2} = 6

Divide both sides

\frac{3 x ^{2}}{3} = \frac{6}{3}

Divide the numbers

x^{2} = \frac{6}{3}

Divide the numbers

More Steps

x^{2} = 2

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

x = \pm 2

Separate the equation into 2 possible cases

x = 2 x = - 2

Determine the test intervals using the critical values

x < - 2 - 2 < x < 2 x > 2

Choose a value form each interval

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

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

More Steps

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

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

More Steps

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

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

More Steps

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

Solution

- 2 < x < 2

Alternative Form

x \in (- 2, 2)

Show Solution