Solve r(\beta )≤r(\alpha 1\alpha 2\alpha 3)

Evaluate

r β \leq r (α \times 1 \times α \times 2 α \times 3)

Remove the parentheses

r β \leq r α \times 1 \times α \times 2 α \times 3

Simplify

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r β \leq 6 r α^{3}

Swap the sides of the inequality

6 r α^{3} \geq r β

Divide both sides

\frac{6 r α ^{3}}{6 r} \geq \frac{r β}{6 r}

Divide the numbers

α^{3} \geq \frac{r β}{6 r}

Divide the numbers

α^{3} \geq \frac{β}{6}

Rewrite the inequalities

{α^{3} \geq \frac{β}{6} r > 0 {α^{3} \leq \frac{β}{6} r < 0

Calculate

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{α \geq \frac{3 36 β}{6} r > 0 {α^{3} \leq \frac{β}{6} r < 0

Calculate

More Steps

{α \geq \frac{3 36 β}{6} r > 0 {α \leq \frac{3 36 β}{6} r < 0

Solution

α \geq \frac{3 36 β}{6}, r > 0 α \leq \frac{3 36 β}{6}, r < 0

Solve the inequality