Solve 6x^3\le33 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for x

x \leq \frac{3 44}{2}

Alternative Form

x \in (- \infty, \frac{3 44}{2}]

Evaluate

6 x^{3} \leq 33

Move the expression to the left side

6 x^{3} - 33 \leq 0

Rewrite the expression

6 x^{3} - 33 = 0

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

6 x^{3} = 0 + 33

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

6 x^{3} = 33

Divide both sides

\frac{6 x ^{3}}{6} = \frac{33}{6}

Divide the numbers

x^{3} = \frac{33}{6}

Cancel out the common factor 3

x^{3} = \frac{11}{2}

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

3 x^{3} = 3 \frac{11}{2}

Calculate

x = 3 \frac{11}{2}

Simplify the root

More Steps

x = \frac{3 44}{2}

Determine the test intervals using the critical values

x < \frac{3 44}{2} x > \frac{3 44}{2}

Choose a value form each interval

x_{1} = 1 x_{2} = 3

To determine if x < \frac{3 44}{2} is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

More Steps

x < \frac{3 44}{2} is the solution x_{2} = 3

To determine if x > \frac{3 44}{2} is the solution to the inequality,test if the chosen value x = 3 satisfies the initial inequality

More Steps

x < \frac{3 44}{2} is the solution x > \frac{3 44}{2} is not a solution

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

x \leq \frac{3 44}{2} is the solution

Solution

x \leq \frac{3 44}{2}

Alternative Form

x \in (- \infty, \frac{3 44}{2}]

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