Let's analyze the work done by Roy and Sam on the equation step by step.
The given equation is:
[tex]\[ -3x + 4 = 5x - 6 \][/tex]
Let's break down what each student did:
### Roy's Work
1. The given equation:
[tex]\[ -3x + 4 = 5x - 6 \][/tex]
2. Roy's next step:
[tex]\[ -3x + 4 - 4 = 5x - 6 - 4 \][/tex]
(He subtracted 4 from both sides to isolate the constant term)
[tex]\[ -3x = 5x - 10 \][/tex]
3. Next, he moved all terms involving [tex]\( x \)[/tex] to one side by subtracting [tex]\( 5x \)[/tex] from both sides:
[tex]\[ -3x - 5x = -10 \][/tex]
[tex]\[ -8x = -10 \][/tex]
This led him to:
[tex]\[ -8x + 4 = -6 \][/tex]
### Sam's Work
1. The given equation:
[tex]\[ -3x + 4 = 5x - 6 \][/tex]
2. Sam's next step:
[tex]\[ -3x + 4 - 4 = 5x - 6 - 4 \][/tex]
[tex]\[ -3x = 5x - 10 \][/tex]
3. Then he subtracted [tex]\( 5x \)[/tex] from both sides to isolate the [tex]\( x \)[/tex]-terms:
[tex]\[ -3x - 5x + 6 = 0 \][/tex]
Now looking at Sam's work:
1. The given equation:
[tex]\[ -3x + 4 = 5x - 6 \][/tex]
2. Sam's next step:
[tex]\[ -3x + 4 - 4 = 5x - 6 - 4 \][/tex]
[tex]\[ -3x = 5x - 10 \][/tex]
By subtracting [tex]\(4\)[/tex] from both sides, we maintain equality.
3. Then he rearranges the terms:
[tex]\[ -3x = 5x - 10 \][/tex]
Now, add/subtract x from both sides if necessary, leading us to isolate the variable.
Sam’s step is:
[tex]\[ 4 = 2x - 6 \][/tex]
Then adding 6:
[tex]\[ 4 + 6 = 2x \][/tex]
[tex]\[ 10 = 2x\][/tex]
Following the steps confirms that to maintain equality, Sam's initial work is indeed correct.
Based on the detailed analysis:
Sam's initial work is correct, and he used the subtraction property of equality.
Therefore, the correct answer is:
c. Sam's work is correct so far. He used the subtraction property of equality.
