To solve the equation [tex]\(\sqrt{3x} - 6 = 6\)[/tex], follow these steps:
1. Isolate the square root term:
Begin by adding 6 to both sides of the equation to get rid of the -6 next to the square root:
[tex]\[
\sqrt{3x} - 6 + 6 = 6 + 6
\][/tex]
Simplifying, we have:
[tex]\[
\sqrt{3x} = 12
\][/tex]
2. Eliminate the square root:
To remove the square root, square both sides of the equation:
[tex]\[
(\sqrt{3x})^2 = 12^2
\][/tex]
This simplifies to:
[tex]\[
3x = 144
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Finally, solve for [tex]\(x\)[/tex] by dividing both sides by 3:
[tex]\[
x = \frac{144}{3}
\][/tex]
Simplifying the right-hand side, we find:
[tex]\[
x = 48
\][/tex]
Therefore, the solution to the equation [tex]\(\sqrt{3x} - 6 = 6\)[/tex] is:
[tex]\[
x = 48
\][/tex]
