Question

which of the following occurs within the solution process for (sqrt3{5x - 2} - sqrt3{4x} = 0)?
options:

• cubing both sides twice
• cubing both sides once
• squaring both sides twice
• squaring both sides once

Explanation:

Step1: Start with the equation

We have the equation \(\sqrt[3]{5x - 2}-\sqrt[3]{4x}=0\). First, we can isolate one of the cube - root terms. Let's add \(\sqrt[3]{4x}\) to both sides of the equation. So we get \(\sqrt[3]{5x - 2}=\sqrt[3]{4x}\).

Step2: Cube both sides

Since we have cube - roots on both sides, to eliminate the cube - root, we cube both sides of the equation \(\sqrt[3]{5x - 2}=\sqrt[3]{4x}\). Recall that \((\sqrt[3]{a})^3=a\) for any real number \(a\). So when we cube the left - hand side \((\sqrt[3]{5x - 2})^3 = 5x-2\), and when we cube the right - hand side \((\sqrt[3]{4x})^3=4x\). After cubing both sides, we get the linear equation \(5x - 2=4x\), and we only need to cube both sides once to solve the equation.

Answer:

B. cubing both sides once (assuming the options are labeled as A: cubing both sides twice, B: cubing both sides once, C: squaring both sides twice, D: squaring both sides once)