Solve -13<b^3-14 - ScanMath

Evaluate

- 13 < b^{3} - 14

Move the expression to the left side

- 13 - (b^{3} - 14) < 0

Subtract the terms

More Steps

1 - b^{3} < 0

Rewrite the expression

1 - b^{3} = 0

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

- b^{3} = 0 - 1

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

- b^{3} = - 1

Change the signs on both sides of the equation

b^{3} = 1

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

3 b^{3} = 31

Calculate

b = 31

Simplify the root

b = 1

Determine the test intervals using the critical values

b < 1 b > 1

Choose a value form each interval

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

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

More Steps

b < 1 is not a solution b_{2} = 2

To determine if b > 1 is the solution to the inequality,test if the chosen value b = 2 satisfies the initial inequality

More Steps

b < 1 is not a solution b > 1 is the solution

Solution

b > 1

Alternative Form

b \in (1, + \infty)

Solve the inequality