Solve (x^2)/2 < 1

Evaluate

\frac{x ^{2}}{2} < 1

Multiply both sides of the inequality by 2

\frac{x ^{2}}{2} \times 2 < 1 \times 2

Multiply the terms

x^{2} < 1 \times 2

Multiply the terms

x^{2} < 2

Move the expression to the left side

x^{2} - 2 < 0

Rewrite the expression

x^{2} - 2 = 0

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

x^{2} = 0 + 2

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

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)

Solve the inequality