Solve 1/4 (8b^3)≤ 6/8

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for b

b \leq \frac{3 3}{2}

Alternative Form

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

Evaluate

\frac{1}{4} \times 8 b^{3} \leq \frac{6}{8}

Multiply the numbers

More Steps

2 b^{3} \leq \frac{6}{8}

Cancel out the common factor 2

2 b^{3} \leq \frac{3}{4}

Move the expression to the left side

2 b^{3} - \frac{3}{4} \leq 0

Rewrite the expression

2 b^{3} - \frac{3}{4} = 0

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

2 b^{3} = 0 + \frac{3}{4}

Add the terms

2 b^{3} = \frac{3}{4}

Multiply by the reciprocal

2 b^{3} \times \frac{1}{2} = \frac{3}{4} \times \frac{1}{2}

Multiply

b^{3} = \frac{3}{4} \times \frac{1}{2}

Multiply

More Steps

b^{3} = \frac{3}{8}

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

3 b^{3} = 3 \frac{3}{8}

Calculate

b = 3 \frac{3}{8}

Simplify the root

More Steps

b = \frac{3 3}{2}

Determine the test intervals using the critical values

b < \frac{3 3}{2} b > \frac{3 3}{2}

Choose a value form each interval

b_{1} = 0 b_{2} = 2

To determine if b < \frac{3 3}{2} is the solution to the inequality,test if the chosen value b = 0 satisfies the initial inequality

More Steps

b < \frac{3 3}{2} is the solution b_{2} = 2

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

More Steps

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

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

b \leq \frac{3 3}{2} is the solution

Solution

b \leq \frac{3 3}{2}

Alternative Form

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

Show Solution