Question

question
lily solved the equation 3x - 10 = -3x + 8. the explanation of her process is shown. select the text that shows an error in her process or justification of steps, if one exists.

1. i used the addition property of equality to achieve 6x - 10 = 8.
2. i used the addition property of equality to achieve 6x = 18.
3. i used the subtraction property of equality to achieve the solution of x = 3.

there is no error in lily’s process or justification of steps.

Explanation:

To solve \(3x - 10=-3x + 8\):

• Step 1: Add \(3x\) to both sides (addition property of equality) gives \(6x - 10 = 8\) (correct).
• Step 2: Add \(10\) to both sides (addition property of equality) gives \(6x=18\) (correct).
• Step 3: To solve \(6x = 18\) for \(x\), we should use the division property of equality (divide both sides by 6) to get \(x = 3\), not the subtraction property of equality. So the justification in step 3 is incorrect.

Answer:

1. I used the subtraction property of equality to achieve the solution of \( x = 3 \).