To solve the equation [tex]\(\frac{(x+16)}{3} = 3x\)[/tex] for [tex]\(x\)[/tex], we can follow a step-by-step approach. Here’s how we can solve it:
1. Multiply both sides of the equation by 3 to eliminate the fraction:
[tex]\[
\frac{(x + 16)}{3} \cdot 3 = 3x \cdot 3
\][/tex]
This simplifies to:
[tex]\[
x + 16 = 9x
\][/tex]
2. Rearrange the equation to isolate [tex]\(x\)[/tex]. Subtract [tex]\(x\)[/tex] from both sides:
[tex]\[
x + 16 - x = 9x - x
\][/tex]
Which simplifies to:
[tex]\[
16 = 8x
\][/tex]
3. Solve for [tex]\(x\)[/tex]. Divide both sides by 8:
[tex]\[
\frac{16}{8} = \frac{8x}{8}
\][/tex]
This simplifies to:
[tex]\[
2 = x
\][/tex]
Therefore, the solution to the equation [tex]\(\frac{(x+16)}{3} = 3x\)[/tex] is [tex]\(x = 2\)[/tex].
None of the other options, [tex]\(x = -7\)[/tex], [tex]\(x = -13\)[/tex], or [tex]\(x = 8\)[/tex], satisfy the equation. The correct solution is indeed [tex]\(x = 2\)[/tex].
