Solve for x 3 = cube root of 2x+16-12

$3 = \sqrt[3]{2 x + 16} - 12$

Step 1

Rewrite the equation as $\sqrt[3]{2 x + 16} - 12 = 3$ .

$\sqrt[3]{2 x + 16} - 12 = 3$

Step 2

Move all terms not containing $\sqrt[3]{2 x + 16}$ to the right side of the equation.

Add $12$ to both sides of the equation.

$\sqrt[3]{2 x + 16} = 3 + 12$

Add $3$ and $12$ .

$\sqrt[3]{2 x + 16} = 15$

Step 3

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

${\sqrt[3]{2 x + 16}}^{3} = 15^{3}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 x + 16}$ as ${(2 x + 16)}^{\frac{1}{3}}$ .

${({(2 x + 16)}^{\frac{1}{3}})}^{3} = 15^{3}$

Simplify the left side.

Simplify ${({(2 x + 16)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(2 x + 16)}^{\frac{1}{3}})}^{3}$ .

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

${(2 x + 16)}^{\frac{1}{3} \cdot 3} = 15^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(2 x + 16)}^{\frac{1}{3} \cdot 3} = 15^{3}$

Rewrite the expression.

${(2 x + 16)}^{1} = 15^{3}$

Simplify.

$2 x + 16 = 15^{3}$

Simplify the right side.

Raise $15$ to the power of $3$ .

$2 x + 16 = 3375$

Step 5

Solve for $x$ .

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

Subtract $16$ from both sides of the equation.

$2 x = 3375 - 16$

Subtract $16$ from $3375$ .

$2 x = 3359$

Divide each term in $2 x = 3359$ by $2$ and simplify.

Divide each term in $2 x = 3359$ by $2$ .

$\frac{2 x}{2} = \frac{3359}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3359}{2}$

Divide $x$ by $1$ .

$x = \frac{3359}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3359}{2}$

Decimal Form:

$x = 1679.5$

Mixed Number Form:

$x = 1679 \frac{1}{2}$

Solve for x 3 = cube root of 2x+16-12

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