Algebra Examples

$\sqrt[3]{x + 5} \geq 2$

Step 1

To remove the radical on the left side of the inequality, cube both sides of the inequality.

${\sqrt[3]{x + 5}}^{3} \geq 2^{3}$

Step 2

Simplify each side of the inequality.

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Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x + 5}$ as ${(x + 5)}^{\frac{1}{3}}$ .

${({(x + 5)}^{\frac{1}{3}})}^{3} \geq 2^{3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${({(x + 5)}^{\frac{1}{3}})}^{3}$ .

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Step 2.2.1.1

Multiply the exponents in ${({(x + 5)}^{\frac{1}{3}})}^{3}$ .

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Step 2.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x + 5)}^{\frac{1}{3} \cdot 3} \geq 2^{3}$

Step 2.2.1.1.2

Cancel the common factor of $3$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

${(x + 5)}^{\frac{1}{3} \cdot 3} \geq 2^{3}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(x + 5)}^{1} \geq 2^{3}$

Step 2.2.1.2

Simplify.

$x + 5 \geq 2^{3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $2$ to the power of $3$ .

$x + 5 \geq 8$

Step 3

Move all terms not containing $x$ to the right side of the inequality.

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Step 3.1

Subtract $5$ from both sides of the inequality.

$x \geq 8 - 5$

Step 3.2

Subtract $5$ from $8$ .

$x \geq 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq 3$

Interval Notation:

$[3, \infty)$

Step 5