The equation [tex]\(\frac{(x+16)}{3}=3x\)[/tex] represents when two tutoring services with different rate plans charge the same fees for a session of [tex]\(x\)[/tex] hours. Solve for [tex]\(x\)[/tex].

A. [tex]\(x = -7\)[/tex]

B. [tex]\(x = -13\)[/tex]

C. [tex]\(x = 8\)[/tex]

D. [tex]\(x = 2\)[/tex]



Answer :

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].