Question

select the correct answer from each drop - down menu. consider this equation. ((4x)^{\frac{1}{3}}-x = 0) the first step in solving this equation is to add x to both sides. solving this equation for x initially yields. checking the solutions shows that the second step is to add the cube root of x to both sides add the cube of x to both sides cube both sides reset next

Explanation:

Step1: Analyze the first step

The equation is \((4x)^{\frac{1}{3}} - x = 0\). To isolate the radical term, we can add \(x\) to both sides. So the first step is to add \(x\) to both sides, which gives \((4x)^{\frac{1}{3}}=x\).

Step2: Analyze the second step

Now that we have \((4x)^{\frac{1}{3}} = x\), to eliminate the cube - root, we cube both sides of the equation. Cubing the left - hand side \(((4x)^{\frac{1}{3}})^3=4x\) and cubing the right - hand side \(x^3\). So the second step is to cube both sides.

Answer:

First step: add x to both sides; Second step: cube both sides