Solve for x 2 cube root of 1-3x+4=6

$2 \sqrt[3]{1 - 3 x} + 4 = 6$

Step 1

Move all terms not containing $2 \sqrt[3]{1 - 3 x}$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$2 \sqrt[3]{1 - 3 x} = 6 - 4$

Subtract $4$ from $6$ .

$2 \sqrt[3]{1 - 3 x} = 2$

Step 2

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

${(2 \sqrt[3]{1 - 3 x})}^{3} = 2^{3}$

Step 3

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

$8 {({(1 - 3 x)}^{\frac{1}{3}})}^{3} = 2^{3}$

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

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

$8 {(1 - 3 x)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$8 {(1 - 3 x)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Rewrite the expression.

$8 {(1 - 3 x)}^{1} = 2^{3}$

Simplify.

$8 (1 - 3 x) = 2^{3}$

Apply the distributive property.

$8 \cdot 1 + 8 (- 3 x) = 2^{3}$

Multiply.

Multiply $8$ by $1$ .

$8 + 8 (- 3 x) = 2^{3}$

Multiply $- 3$ by $8$ .

$8 - 24 x = 2^{3}$

Simplify the right side.

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

$8 - 24 x = 8$

Step 4

Solve for $x$ .

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

Subtract $8$ from both sides of the equation.

$- 24 x = 8 - 8$

Subtract $8$ from $8$ .

$- 24 x = 0$

Divide each term in $- 24 x = 0$ by $- 24$ and simplify.

Divide each term in $- 24 x = 0$ by $- 24$ .

$\frac{- 24 x}{- 24} = \frac{0}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 x}{- 24} = \frac{0}{- 24}$

Divide $x$ by $1$ .

$x = \frac{0}{- 24}$

Simplify the right side.

Divide $0$ by $- 24$ .

$x = 0$

Solve for x 2 cube root of 1-3x+4=6

Related Questions

Support LCMGCF.com by disabling your adblocker.