Solve r^59≥-20 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for r

r \geq - \frac{5 540}{3}

Alternative Form

r \in [- \frac{5 540}{3}, + \infty)

Evaluate

r^{5} \times 9 \geq - 20

Use the commutative property to reorder the terms

9 r^{5} \geq - 20

Move the expression to the left side

9 r^{5} - (- 20) \geq 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

9 r^{5} + 20 \geq 0

Rewrite the expression

9 r^{5} + 20 = 0

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

9 r^{5} = 0 - 20

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

9 r^{5} = - 20

Divide both sides

\frac{9 r ^{5}}{9} = \frac{- 20}{9}

Divide the numbers

r^{5} = \frac{- 20}{9}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

r^{5} = - \frac{20}{9}

Take the 5 -th root on both sides of the equation

5 r^{5} = 5 - \frac{20}{9}

Calculate

r = 5 - \frac{20}{9}

Simplify the root

More Steps

r = - \frac{5 540}{3}

Determine the test intervals using the critical values

r < - \frac{5 540}{3} r > - \frac{5 540}{3}

Choose a value form each interval

r_{1} = - 2 r_{2} = 0

To determine if r < - \frac{5 540}{3} is the solution to the inequality,test if the chosen value r = - 2 satisfies the initial inequality

More Steps

r < - \frac{5 540}{3} is not a solution r_{2} = 0

To determine if r > - \frac{5 540}{3} is the solution to the inequality,test if the chosen value r = 0 satisfies the initial inequality

More Steps

r < - \frac{5 540}{3} is not a solution r > - \frac{5 540}{3} is the solution

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

r \geq - \frac{5 540}{3} is the solution

Solution

r \geq - \frac{5 540}{3}

Alternative Form

r \in [- \frac{5 540}{3}, + \infty)

Show Solution