Solve 1/9x x- 2/3>0

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \in (- \infty, - 6) \cup (6, + \infty)

Evaluate

\frac{1}{9} x \times x - \frac{2}{3} > 0

Multiply the terms

\frac{1}{9} x^{2} - \frac{2}{3} > 0

Rewrite the expression

\frac{1}{9} x^{2} - \frac{2}{3} = 0

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

\frac{1}{9} x^{2} = 0 + \frac{2}{3}

Add the terms

\frac{1}{9} x^{2} = \frac{2}{3}

Multiply by the reciprocal

\frac{1}{9} x^{2} \times 9 = \frac{2}{3} \times 9

Multiply

x^{2} = \frac{2}{3} \times 9

Multiply

More Steps

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

Solution

x \in (- \infty, - 6) \cup (6, + \infty)

Show Solution