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9. Solve 3x+2b=6c

for x.

Step 1: 3x+2b−2b=6c−2b
subtract 2b from both sides

Step 2: 3x=6c−2b
combine like terms/simplify

Step 3: 3x3=6c3−2b
divide by 3 on both sides to get x isolated

Step 4: x=2c−2b
simplify/final answer

Which statement is TRUE?

(1 point)
Responses

The process has an error. The correct answer is x=4bc/3

The process is correct.

The process has an error. The correct answer is x=2c−2/3b

The process has an error. The correct answer is x=−4b−c

1 answer

Let's review the steps provided for solving the equation \(3x + 2b = 6c\) for \(x\) to see if there are any errors.

  1. Starting equation:
    \[3x + 2b = 6c\]

  2. Step 1: Subtract \(2b\) from both sides:
    \[3x + 2b - 2b = 6c - 2b\]
    This simplifies correctly to:
    \[3x = 6c - 2b\]

  3. Step 2: Rename equation (just renaming):
    \[3x = 6c - 2b\]
    (This statement is correct; there's no need to label this as combining like terms; it's now ready for the next step.)

  4. Step 3: Divide both sides by 3:
    \[\frac{3x}{3} = \frac{6c - 2b}{3}\]
    This correctly becomes:
    \[x = \frac{6c - 2b}{3}\]

  5. Step 4: Simplify:
    \[x = \frac{6c}{3} - \frac{2b}{3}\]
    This simplifies to:
    \[x = 2c - \frac{2b}{3}\]

Based on the steps above, the correction from the initial process leads us to the following correct conclusion: \[x = 2c - \frac{2b}{3}\]

Now, checking the options given:

  • The process has an error. The correct answer is \(x = 4bc/3\) - False
  • The process is correct. - False (The process led to the wrong final conclusion)
  • The process has an error. The correct answer is \(x = 2c - \frac{2}{3}b\) - True
  • The process has an error. The correct answer is \(x = -4b - c\) - False

Therefore, the TRUE statement is: The process has an error. The correct answer is \(x = 2c - \frac{2}{3}b\).