Question

Solve this equation for X. If necessary, round your answer to the nearest integer$(2x + 2)^{ \frac{1 }{3} = - 2$

Answer 1

Answer

x = 1

Explanation:

Given the following equation

$\begin{gathered} (2x+2)^{\frac{1}{2}}=\text{ -2} \\ \text{According to the law of indicies} \\ x^{\frac{1}{2}}\text{ = }\sqrt[]{x} \\ (2x+2)^{\frac{1}{2}}\text{ = }\sqrt[]{(2x\text{ + 2)}} \\ \text{Step 1: Take the square of both sides} \\ \sqrt[]{(2x\text{ + 2) }}\text{ = -2} \\ \sqrt[]{(2x+2)^2}=-2^2 \\ 2x\text{ + 2 = 4} \\ \text{Collect the like terms} \\ 2x\text{ = 4 - 2} \\ 2x\text{ = 2} \\ \text{Divide both sides by 2} \\ \frac{2x}{2}\text{ = }\frac{2}{2} \\ x\text{ = 1} \end{gathered}$

Therefore, x = 1