Solve for x 12 cube root of 2x-7=21

$12 \sqrt[3]{2 x - 7} = 21$

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

${(12 \sqrt[3]{2 x - 7})}^{3} = 21^{3}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 x - 7}$ as ${(2 x - 7)}^{\frac{1}{3}}$ .

${(12 {(2 x - 7)}^{\frac{1}{3}})}^{3} = 21^{3}$

Simplify the left side.

Simplify ${(12 {(2 x - 7)}^{\frac{1}{3}})}^{3}$ .

Apply the product rule to $12 {(2 x - 7)}^{\frac{1}{3}}$ .

$12^{3} {({(2 x - 7)}^{\frac{1}{3}})}^{3} = 21^{3}$

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

$1728 {({(2 x - 7)}^{\frac{1}{3}})}^{3} = 21^{3}$

Multiply the exponents in ${({(2 x - 7)}^{\frac{1}{3}})}^{3}$ .

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

$1728 {(2 x - 7)}^{\frac{1}{3} \cdot 3} = 21^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$1728 {(2 x - 7)}^{\frac{1}{3} \cdot 3} = 21^{3}$

Rewrite the expression.

$1728 {(2 x - 7)}^{1} = 21^{3}$

Simplify.

$1728 (2 x - 7) = 21^{3}$

Apply the distributive property.

$1728 (2 x) + 1728 \cdot - 7 = 21^{3}$

Multiply.

Multiply $2$ by $1728$ .

$3456 x + 1728 \cdot - 7 = 21^{3}$

Multiply $1728$ by $- 7$ .

$3456 x - 12096 = 21^{3}$

Simplify the right side.

Raise $21$ to the power of $3$ .

$3456 x - 12096 = 9261$

Solve for $x$ .

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

Add $12096$ to both sides of the equation.

$3456 x = 9261 + 12096$

Add $9261$ and $12096$ .

$3456 x = 21357$

Divide each term in $3456 x = 21357$ by $3456$ and simplify.

Divide each term in $3456 x = 21357$ by $3456$ .

$\frac{3456 x}{3456} = \frac{21357}{3456}$

Simplify the left side.

Cancel the common factor of $3456$ .

Cancel the common factor.

$\frac{3456 x}{3456} = \frac{21357}{3456}$

Divide $x$ by $1$ .

$x = \frac{21357}{3456}$

Simplify the right side.

Cancel the common factor of $21357$ and $3456$ .

Factor $27$ out of $21357$ .

$x = \frac{27 (791)}{3456}$

Cancel the common factors.

Factor $27$ out of $3456$ .

$x = \frac{27 \cdot 791}{27 \cdot 128}$

Cancel the common factor.

$x = \frac{27 \cdot 791}{27 \cdot 128}$

Rewrite the expression.

$x = \frac{791}{128}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{791}{128}$

Decimal Form:

$x = 6.1796875$

Mixed Number Form:

$x = 6 \frac{23}{128}$

Solve for x 12 cube root of 2x-7=21

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