Solve x^2/3<2 - ScanMath

Evaluate

\frac{x ^{2}}{3} < 2

Multiply both sides of the inequality by 3

\frac{x ^{2}}{3} \times 3 < 2 \times 3

Multiply the terms

x^{2} < 2 \times 3

Multiply the terms

x^{2} < 6

Move the expression to the left side

x^{2} - 6 < 0

Rewrite the expression

x^{2} - 6 = 0

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

x^{2} = 0 + 6

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

x^{2} = 6

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

x = \pm 6

Separate the equation into 2 possible cases

x = 6 x = - 6

Determine the test intervals using the critical values

x < - 6 - 6 < x < 6 x > 6

Choose a value form each interval

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

To determine if x < - 6 is the solution to the inequality,test if the chosen value x = - 3 satisfies the initial inequality

More Steps

x < - 6 is not a solution x_{2} = 0 x_{3} = 3

To determine if - 6 < x < 6 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 6 is not a solution - 6 < x < 6 is the solution x_{3} = 3

To determine if x > 6 is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < - 6 is not a solution - 6 < x < 6 is the solution x > 6 is not a solution

Solution

- 6 < x < 6

Alternative Form

x \in (- 6, 6)

Solve the inequality