To solve the given equation [tex]\(\sqrt{6x + 4} = 8\)[/tex], we follow these steps in order:
1. Step F: Square both sides
We need to eliminate the square root by squaring both sides of the equation.
[tex]\[
(\sqrt{6x + 4})^2 = 8^2
\][/tex]
This simplifies to:
[tex]\[
6x + 4 = 64
\][/tex]
2. Step D: Subtract 4 from both sides
Next, we need to isolate the term containing [tex]\(x\)[/tex]. To do this, we subtract 4 from both sides.
[tex]\[
6x + 4 - 4 = 64 - 4
\][/tex]
This simplifies to:
[tex]\[
6x = 60
\][/tex]
3. Step C: Divide by 6 from both sides
Finally, we solve for [tex]\(x\)[/tex] by dividing both sides by 6.
[tex]\[
\frac{6x}{6} = \frac{60}{6}
\][/tex]
This simplifies to:
[tex]\[
x = 10
\][/tex]
Thus, the correct order of steps to solve [tex]\(\sqrt{6x + 4} = 8\)[/tex] is:
- First [tex]\(F\)[/tex]: Square both sides
- Then [tex]\(D\)[/tex]: Subtract 4 from both sides
- Finally [tex]\(C\)[/tex]: Divide by 6 from both sides
So the correct answer is:
First F, then D, then C.
