Solve (x^2)/3 >4 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \in (- \infty, - 23) \cup (23, + \infty)

Evaluate

\frac{x ^{2}}{3} > 4

Multiply both sides of the inequality by 3

\frac{x ^{2}}{3} \times 3 > 4 \times 3

Multiply the terms

x^{2} > 4 \times 3

Multiply the terms

x^{2} > 12

Move the expression to the left side

x^{2} - 12 > 0

Rewrite the expression

x^{2} - 12 = 0

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

x^{2} = 0 + 12

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

x^{2} = 12

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

x = \pm 12

Simplify the expression

More Steps

x = \pm 23

Separate the equation into 2 possible cases

x = 23 x = - 23

Determine the test intervals using the critical values

x < - 23 - 23 < x < 23 x > 23

Choose a value form each interval

x_{1} = - 4 x_{2} = 0 x_{3} = 4

To determine if x < - 23 is the solution to the inequality,test if the chosen value x = - 4 satisfies the initial inequality

More Steps

x < - 23 is the solution x_{2} = 0 x_{3} = 4

To determine if - 23 < x < 23 is the solution to the inequality,test if the chosen value x = 0 satisfies the initial inequality

More Steps

x < - 23 is the solution - 23 < x < 23 is not a solution x_{3} = 4

To determine if x > 23 is the solution to the inequality,test if the chosen value x = 4 satisfies the initial inequality

More Steps

x < - 23 is the solution - 23 < x < 23 is not a solution x > 23 is the solution

Solution

x \in (- \infty, - 23) \cup (23, + \infty)

Show Solution