Solve 6x^22x 9 ≤ 1

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \leq \frac{3 2}{6}

Alternative Form

x \in (- \infty, \frac{3 2}{6}]

Evaluate

6 x^{2} \times 2 x \times 9 \leq 1

Multiply

More Steps

108 x^{3} \leq 1

Move the expression to the left side

108 x^{3} - 1 \leq 0

Rewrite the expression

108 x^{3} - 1 = 0

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

108 x^{3} = 0 + 1

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

108 x^{3} = 1

Divide both sides

\frac{108 x ^{3}}{108} = \frac{1}{108}

Divide the numbers

x^{3} = \frac{1}{108}

Take the 3 -th root on both sides of the equation

3 x^{3} = 3 \frac{1}{108}

Calculate

x = 3 \frac{1}{108}

Simplify the root

More Steps

x = \frac{3 2}{6}

Determine the test intervals using the critical values

x < \frac{3 2}{6} x > \frac{3 2}{6}

Choose a value form each interval

x_{1} = - 1 x_{2} = 1

To determine if x < \frac{3 2}{6} is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

More Steps

x < \frac{3 2}{6} is the solution x_{2} = 1

To determine if x > \frac{3 2}{6} is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < \frac{3 2}{6} is the solution x > \frac{3 2}{6} is not a solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

x \leq \frac{3 2}{6} is the solution

Solution

x \leq \frac{3 2}{6}

Alternative Form

x \in (- \infty, \frac{3 2}{6}]

Show Solution