Solve for x -2 cube root of x+4<12

$- 2 \sqrt[3]{x + 4} < 12$

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

${(- 2 \sqrt[3]{x + 4})}^{3} < 12^{3}$

Simplify each side of the inequality.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x + 4}$ as ${(x + 4)}^{\frac{1}{3}}$ .

${(- 2 {(x + 4)}^{\frac{1}{3}})}^{3} < 12^{3}$

Simplify the left side.

Simplify ${(- 2 {(x + 4)}^{\frac{1}{3}})}^{3}$ .

Apply the product rule to $- 2 {(x + 4)}^{\frac{1}{3}}$ .

${(- 2)}^{3} {({(x + 4)}^{\frac{1}{3}})}^{3} < 12^{3}$

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

$- 8 {({(x + 4)}^{\frac{1}{3}})}^{3} < 12^{3}$

Multiply the exponents in ${({(x + 4)}^{\frac{1}{3}})}^{3}$ .

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

$- 8 {(x + 4)}^{\frac{1}{3} \cdot 3} < 12^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 8 {(x + 4)}^{\frac{1}{3} \cdot 3} < 12^{3}$

Rewrite the expression.

$- 8 {(x + 4)}^{1} < 12^{3}$

Simplify.

$- 8 (x + 4) < 12^{3}$

Apply the distributive property.

$- 8 x - 8 \cdot 4 < 12^{3}$

Multiply $- 8$ by $4$ .

$- 8 x - 32 < 12^{3}$

Simplify the right side.

Raise $12$ to the power of $3$ .

$- 8 x - 32 < 1728$

Solve for $x$ .

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

Add $32$ to both sides of the inequality.

$- 8 x < 1728 + 32$

Add $1728$ and $32$ .

$- 8 x < 1760$

Divide each term in $- 8 x < 1760$ by $- 8$ and simplify.

Divide each term in $- 8 x < 1760$ by $- 8$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 8 x}{- 8} > \frac{1760}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} > \frac{1760}{- 8}$

Divide $x$ by $1$ .

$x > \frac{1760}{- 8}$

Simplify the right side.

Divide $1760$ by $- 8$ .

$x > - 220$

The result can be shown in multiple forms.

Inequality Form:

$x > - 220$

Interval Notation:

$(- 220, \infty)$

Solve for x -2 cube root of x+4<12

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