Solve -2h^3<-1 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for h

h > \frac{3 4}{2}

Alternative Form

h \in (\frac{3 4}{2}, + \infty)

Evaluate

- 2 h^{3} < - 1

Move the expression to the left side

- 2 h^{3} - (- 1) < 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 2 h^{3} + 1 < 0

Rewrite the expression

- 2 h^{3} + 1 = 0

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

- 2 h^{3} = 0 - 1

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

- 2 h^{3} = - 1

Change the signs on both sides of the equation

2 h^{3} = 1

Divide both sides

\frac{2 h ^{3}}{2} = \frac{1}{2}

Divide the numbers

h^{3} = \frac{1}{2}

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

3 h^{3} = 3 \frac{1}{2}

Calculate

h = 3 \frac{1}{2}

Simplify the root

More Steps

h = \frac{3 4}{2}

Determine the test intervals using the critical values

h < \frac{3 4}{2} h > \frac{3 4}{2}

Choose a value form each interval

h_{1} = 0 h_{2} = 2

To determine if h < \frac{3 4}{2} is the solution to the inequality,test if the chosen value h = 0 satisfies the initial inequality

More Steps

h < \frac{3 4}{2} is not a solution h_{2} = 2

To determine if h > \frac{3 4}{2} is the solution to the inequality,test if the chosen value h = 2 satisfies the initial inequality

More Steps

h < \frac{3 4}{2} is not a solution h > \frac{3 4}{2} is the solution

Solution

h > \frac{3 4}{2}

Alternative Form

h \in (\frac{3 4}{2}, + \infty)

Show Solution