Let's carefully solve the equation step-by-step to see whose work is correct and what property was used:
Given equation:
[tex]\[ -3x + 4 = 5x - 6 \][/tex]
### Step 1: Move all the [tex]\( x \)[/tex] terms to one side of the equation.
To do this, we add [tex]\( 3x \)[/tex] to both sides:
[tex]\[ -3x + 3x + 4 = 5x + 3x - 6 \][/tex]
This simplifies to:
[tex]\[ 4 = 8x - 6 \][/tex]
### Step 2: Move the constant terms to the other side of the equation.
To do this, we add 6 to both sides:
[tex]\[ 4 + 6 = 8x - 6 + 6 \][/tex]
This simplifies to:
[tex]\[ 10 = 8x \][/tex]
### Step 3: Solve for [tex]\( x \)[/tex].
To find [tex]\( x \)[/tex], we divide both sides by 8:
[tex]\[ \frac{10}{8} = \frac{8x}{8} \][/tex]
This simplifies to:
[tex]\[ x = \frac{5}{4} \][/tex]
[tex]\[ x = 1.25 \][/tex]
The steps used to isolate the variable [tex]\( x \)[/tex] involved:
1. Adding [tex]\( 3x \)[/tex] to both sides to combine the [tex]\( x \)[/tex] terms.
2. Adding 6 to both sides to move the constant term to the other side.
The first step in moving the [tex]\( x \)[/tex] terms involved the addition property of equality because we added the same value [tex]\( 3x \)[/tex] to both sides of the equation to keep it balanced.
Therefore, the correct answer is:
A. Sam's work is correct so far. He used the addition property of equality.
