Sure, let's solve the equation step-by-step to find the value of [tex]\( x \)[/tex].
We start with the given equation:
[tex]\[ \frac{x + 16}{3} = 3x \][/tex]
Step 1: Eliminate the fraction by multiplying both sides of the equation by 3:
[tex]\[ 3 \cdot \frac{x + 16}{3} = 3 \cdot 3x \][/tex]
[tex]\[ x + 16 = 9x \][/tex]
Step 2: Move all terms involving [tex]\( x \)[/tex] to one side of the equation. Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[ x + 16 - x = 9x - x \][/tex]
[tex]\[ 16 = 8x \][/tex]
Step 3: Solve for [tex]\( x \)[/tex] by dividing both sides by 8:
[tex]\[ \frac{16}{8} = \frac{8x}{8} \][/tex]
[tex]\[ 2 = x \][/tex]
So the solution for [tex]\( x \)[/tex] is:
[tex]\[ x = 2 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] that makes the two tutoring services charge the same fee for a session is [tex]\( x = 2 \)[/tex] hours.
