Solve by Factoring cube root of 2x+5=2

$\sqrt[3]{2 x + 5} = 2$

Step 1

Subtract $2$ from both sides of the equation.

$\sqrt[3]{2 x + 5} - 2 = 0$

Step 2

Add $2$ to both sides of the equation.

$\sqrt[3]{2 x + 5} = 2$

Step 3

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

${\sqrt[3]{2 x + 5}}^{3} = 2^{3}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 x + 5}$ as ${(2 x + 5)}^{\frac{1}{3}}$ .

${({(2 x + 5)}^{\frac{1}{3}})}^{3} = 2^{3}$

Simplify the left side.

Simplify ${({(2 x + 5)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(2 x + 5)}^{\frac{1}{3}})}^{3}$ .

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

${(2 x + 5)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(2 x + 5)}^{\frac{1}{3} \cdot 3} = 2^{3}$

Rewrite the expression.

${(2 x + 5)}^{1} = 2^{3}$

Simplify.

$2 x + 5 = 2^{3}$

Simplify the right side.

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

$2 x + 5 = 8$

Step 5

Solve for $x$ .

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

Subtract $5$ from both sides of the equation.

$2 x = 8 - 5$

Subtract $5$ from $8$ .

$2 x = 3$

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2}$