Liliana solved the equation below. When she tried to verify her answer, she realized she made an error.

Question

One-third (x + 18) = 7
One-third x + 6 = 7
One-third x + 6 minus 6 = 7 + 6
One-third x = 1
x = 3

Which correction should Liliana make?
The first step should be One-third x + 54 = 7.
The second step should be One-third x + 6 minus 6 = 7 minus 6.
The third step should be One-third x = 13.
The final step should be x = one-third.

Answer 1

Let's analyze Liliana's original equation and her steps to find where she went wrong:

The equation is: \[ \frac{1}{3}(x + 18) = 7 \]

1. Correct first step: Liliana's assertion that "One-third (x + 18) = 7" is correct. However, her next step should be to distribute the \(\frac{1}{3}\) through the parentheses: \[ \frac{1}{3}x + 6 = 7 \] This matches her second step, so this part is correct.

2. Incorrect arithmetic in the second step: Here, she attempts to subtract 6 from both sides, but she writes: \[ \frac{1}{3}x + 6 \text{ minus } 6 = 7 + 6 \] This is incorrect. The correct operation should be: \[ \frac{1}{3}x + 6 - 6 = 7 - 6. \] So: \[ \frac{1}{3}x = 1. \]

3. Computing the value of x: Now, using the correct equation: \[ \frac{1}{3}x = 1 \] To isolate \(x\), we multiply both sides by 3: \[ x = 3. \]

Thus, her final step was correct in obtaining \(x = 3\); however, since she misapplied the subtraction, the relevant correction she needs to make is:

The second step should be "One-third x + 6 minus 6 = 7 minus 6."

Regarding the listed options, the appropriate choice for correction is:

The second step should be One-third x + 6 minus 6 = 7 minus 6.