Let's work through the solution step-by-step:
[tex]$
7x - \frac{1}{2}(8x + 2) = 6
$[/tex]
### Step 1: Apply the Distributive Property
We need to distribute [tex]\(\frac{1}{2}\)[/tex] across the expression inside the parentheses.
[tex]$
7x - \frac{1}{2} \cdot 8x - \frac{1}{2} \cdot 2 = 6
$[/tex]
Simplifying this, we get:
[tex]$
7x - 4x - 1 = 6
$[/tex]
Justification: Distributive property
### Step 2: Combine Like Terms
We combine the like terms [tex]\(7x\)[/tex] and [tex]\(-4x\)[/tex].
[tex]$
(7x - 4x) - 1 = 6
$[/tex]
This simplifies to:
[tex]$
3x - 1 = 6
$[/tex]
Justification: Combine like terms
### Step 3: Move the Constant to the Other Side of the Equation
We add 1 to both sides of the equation to isolate the term with [tex]\(x\)[/tex] on one side:
[tex]$
3x - 1 + 1 = 6 + 1
$[/tex]
This simplifies to:
[tex]$
3x = 7
$[/tex]
Justification: Addition property of equality
### Step 4: Divide Both Sides by 3 to Isolate [tex]\(x\)[/tex]
Now, we divide both sides of the equation by 3 to solve for [tex]\(x\)[/tex]:
[tex]$
x = \frac{7}{3}
$[/tex]
Justification: Division property of equality
Based on the detailed solution steps and their justifications, the correct list of justifications Kelsey used to solve the equation is:
1. Distributive property
2. Combine like terms
3. Addition property of equality
4. Division property of equality
Thus, the correct option is:
1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality
