Solve for x 3+ cube root of 5x-6=4

$3 + \sqrt[3]{5 x - 6} = 4$

Step 1

Move all terms not containing $\sqrt[3]{5 x - 6}$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$\sqrt[3]{5 x - 6} = 4 - 3$

Subtract $3$ from $4$ .

$\sqrt[3]{5 x - 6} = 1$

Step 2

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

${\sqrt[3]{5 x - 6}}^{3} = 1^{3}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{5 x - 6}$ as ${(5 x - 6)}^{\frac{1}{3}}$ .

${({(5 x - 6)}^{\frac{1}{3}})}^{3} = 1^{3}$

Simplify the left side.

Simplify ${({(5 x - 6)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(5 x - 6)}^{\frac{1}{3}})}^{3}$ .

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

${(5 x - 6)}^{\frac{1}{3} \cdot 3} = 1^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(5 x - 6)}^{\frac{1}{3} \cdot 3} = 1^{3}$

Rewrite the expression.

${(5 x - 6)}^{1} = 1^{3}$

Simplify.

$5 x - 6 = 1^{3}$

Simplify the right side.

One to any power is one.

$5 x - 6 = 1$

Step 4

Solve for $x$ .

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

Add $6$ to both sides of the equation.

$5 x = 1 + 6$

Add $1$ and $6$ .

$5 x = 7$

Divide each term in $5 x = 7$ by $5$ and simplify.

Divide each term in $5 x = 7$ by $5$ .

$\frac{5 x}{5} = \frac{7}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{7}{5}$

Divide $x$ by $1$ .

$x = \frac{7}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{5}$

Decimal Form:

$x = 1.4$

Mixed Number Form:

$x = 1 \frac{2}{5}$

Solve for x 3+ cube root of 5x-6=4

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