Let's solve the given equation step-by-step and identify where Ray made an error.
The given equation is:
[tex]\[ 3(x+6) = x+8+x \][/tex]
First, expand and simplify both sides of the equation.
Step 1: Expand
[tex]\[ 3(x + 6) = x + 8 + x \][/tex]
[tex]\[ 3x + 18 = 2x + 8 \][/tex]
Ray's first step is correct:
[tex]\[ \text{Step 1: } 3x + 18 = 2x + 8 \][/tex]
Step 2: Subtract [tex]\(2x\)[/tex] from both sides to isolate [tex]\(x\)[/tex] on one side.
[tex]\[ 3x + 18 - 2x = 2x + 8 - 2x \][/tex]
[tex]\[ x + 18 = 8 \][/tex]
At this point, it seems Ray made an error. Instead of correctly isolating [tex]\(x\)[/tex], he incorrectly combined terms that shouldn't be combined.
Ray's incorrect step 2:
[tex]\[ \text{Ray's Step 2: } 5x + 18 = 8 \][/tex]
Step 3: Continue solving the correct equation
[tex]\[ x + 18 = 8 \][/tex]
Subtract 18 from both sides:
[tex]\[ x + 18 - 18 = 8 - 18 \][/tex]
[tex]\[ x = -10 \][/tex]
Ray's steps deviated from the correct process here. Therefore, the error occurred in Step 2.
So, the correct answer is:
B. Step 2
