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Ray made an error while solving the following equation.

Equation: [tex]3(x+6) = x+8+x[/tex]

Step 1: [tex]3x + 18 = 2x + 8[/tex]

Step 2: [tex]5x + 18 = 8[/tex]

Step 3: [tex]5x = -10[/tex]

Step 4: [tex]x = -2[/tex]

In which step did Ray make an error?

A. Step 1
B. Step 2
C. Step 3
D. Step 4

Sagot :

GinnyAnsweridn
Let's examine each step that Ray took while solving the equation to identify where he made an error.

The original equation is:
[tex]\[ 3(x + 6) = x + 8 + x \][/tex]

### Step 1:
Ray transforms the equation as follows:
[tex]\[ 3(x + 6) = x + 8 + x \][/tex]
Simplifying each side, we get:
[tex]\[ 3x + 18 = 2x + 8 \][/tex]

Step 1 is correct so far.

### Step 2:
Ray continues:
[tex]\[ 5x + 18 = 8 \][/tex]

This step is incorrect. Let’s find the right approach from the result of Step 1. We have:
[tex]\[ 3x + 18 = 2x + 8 \][/tex]
Subtracting [tex]\(2x\)[/tex] from both sides:
[tex]\[ x + 18 = 8 \][/tex]

Clearly, Ray made an incorrect transformation here as he mistakenly combined [tex]\(3x\)[/tex] and [tex]\(2x\)[/tex] to [tex]\(5x\)[/tex]. Therefore, the error occurs in Step 2.

By subtracting 2x from both sides, we should have:
[tex]\[ x + 18 = 8 \][/tex]

### Steps 3 and 4 (not revisited, since Step 2 is already determined to be the error):
From the corrected equation [tex]\(x + 18 = 8\)[/tex], we subtract 18 from both sides:
[tex]\[ x = 8 - 18 \][/tex]
[tex]\[ x = -10 \][/tex]

Looking at Ray's steps, the error occurred when Ray wrongly combined the terms in Step 2.

So, Ray made an error in Step 2.

Thus, the answer is:
B. Step 2
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