Solve -1≥y^3 - ScanMath

Evaluate

- 1 \geq y^{3}

Move the expression to the left side

- 1 - y^{3} \geq 0

Rewrite the expression

- 1 - y^{3} = 0

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

- y^{3} = 0 + 1

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

- y^{3} = 1

Change the signs on both sides of the equation

y^{3} = - 1

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

3 y^{3} = 3 - 1

Calculate

y = 3 - 1

Simplify the root

More Steps

y = - 1

Determine the test intervals using the critical values

y < - 1 y > - 1

Choose a value form each interval

y_{1} = - 2 y_{2} = 0

To determine if y < - 1 is the solution to the inequality,test if the chosen value y = - 2 satisfies the initial inequality

More Steps

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

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

More Steps

y < - 1 is the solution y > - 1 is not a solution

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

y \leq - 1 is the solution

Solution

y \leq - 1

Alternative Form

y \in (- \infty, - 1]

Solve the inequality