Question

Alice solved the following equation:

-18 - 3x = 12
-3x = 6
x =-2

Which of the following statements is true?

The 6 should be -6 in step two.
Alice is correct.
The 6 should be -4 in step two.
The 6 should be 30 in step two.

Answer 1

Let's analyze the equation step by step:

Starting with the original equation:
\[
-18 - 3x = 12
\]

To isolate the term with \( x \), we can add 18 to both sides:
\[
-3x = 12 + 18
\]
\[
-3x = 30
\]

Now, dividing both sides by -3 gives:
\[
x = \frac{30}{-3} = -10
\]

So Alice's calculation has an error. The correct value for \( x \) should be -10, not -2.

Now, looking at the options provided:
1. **The 6 should be -6 in step two.** (this is incorrect, as it should actually be 30)
2. **Alice is correct.** (not true, since Alice computed \( x = -2 \), but it should be \( x = -10 \))
3. **The 6 should be -4 in step two.** (also incorrect, since the intermediate result is 30)
4. **The 6 should be 30 in step two.** (this statement is true)

Thus, the correct answer is:
**The 6 should be 30 in step two.**