College

What is the first step in solving the equation [tex]\sqrt[12]{7x^9+4x^2}+4=2[/tex]?

Enter the option number of the correct response.

Option #1: Raise both sides of the equation to the 12th power.
Option #2: Factor [tex]x^2[/tex] out from [tex]7x^9+4x^2[/tex].
Option #3: Subtract 4 from both sides of the equation.

Option # [tex]\square[/tex]

Answer :

To solve the equation [tex]\(\sqrt[12]{7x^9+4x^2}+4=2\)[/tex], we need to break it down step by step to isolate the variable [tex]\(x\)[/tex]. Here’s how you can approach this:

1. Isolate the Radical Expression:
The first step is to get rid of the constant on the same side as the radical. In this equation, we have [tex]\(\sqrt[12]{7x^9+4x^2} + 4 = 2\)[/tex]. To do this, subtract 4 from both sides of the equation:

[tex]\[
\sqrt[12]{7x^9+4x^2} = 2 - 4
\][/tex]

Simplifying the right-hand side gives:

[tex]\[
\sqrt[12]{7x^9+4x^2} = -2
\][/tex]

By following this step, we have effectively isolated the radical expression, which is the essential first step in solving this type of equation.

Therefore, the correct option to start with is:
- Option #3: Subtract 4 from both sides of the equation.