Solve 8y^(2) 3y≤-4(8y^3)

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for y

y \leq 0

Alternative Form

y \in (- \infty, 0]

Evaluate

8 y^{2} \times 3 y \leq - 4 \times 8 y^{3}

Multiply

More Steps

24 y^{3} \leq - 4 \times 8 y^{3}

Multiply the numbers

24 y^{3} \leq - 32 y^{3}

Move the expression to the left side

24 y^{3} - (- 32 y^{3}) \leq 0

Subtract the terms

More Steps

56 y^{3} \leq 0

Rewrite the expression

56 y^{3} = 0

Rewrite the expression

y^{3} = 0

The only way a power can be 0 is when the base equals 0

y = 0

Determine the test intervals using the critical values

y < 0 y > 0

Choose a value form each interval

y_{1} = - 1 y_{2} = 1

To determine if y < 0 is the solution to the inequality,test if the chosen value y = - 1 satisfies the initial inequality

More Steps

y < 0 is the solution y_{2} = 1

To determine if y > 0 is the solution to the inequality,test if the chosen value y = 1 satisfies the initial inequality

More Steps

y < 0 is the solution y > 0 is not a solution

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

y \leq 0 is the solution

Solution

y \leq 0

Alternative Form

y \in (- \infty, 0]

Show Solution