Solve 7(u^3)<-7 - ScanMath

Evaluate

7 u^{3} < - 7

Move the expression to the left side

7 u^{3} - (- 7) < 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

7 u^{3} + 7 < 0

Rewrite the expression

7 u^{3} + 7 = 0

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

7 u^{3} = 0 - 7

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

7 u^{3} = - 7

Divide both sides

\frac{7 u ^{3}}{7} = \frac{- 7}{7}

Divide the numbers

u^{3} = \frac{- 7}{7}

Divide the numbers

More Steps

u^{3} = - 1

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

3 u^{3} = 3 - 1

Calculate

u = 3 - 1

Simplify the root

More Steps

u = - 1

Determine the test intervals using the critical values

u < - 1 u > - 1

Choose a value form each interval

u_{1} = - 2 u_{2} = 0

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

More Steps

u < - 1 is the solution u_{2} = 0

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

More Steps

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

Solution

u < - 1

Alternative Form

u \in (- \infty, - 1)

Solve the inequality