Let's go through the steps Kelsey used to solve the equation [tex]\(7x - \frac{1}{2}(8x + 2) = 6\)[/tex] and understand the justifications for each step:
1. The initial equation is:
[tex]\[
7x - \frac{1}{2}(8x + 2) = 6
\][/tex]
2. Step 1: Distribute [tex]\(\frac{1}{2}\)[/tex] to both terms inside the parentheses:
[tex]\[
7x - 4x - 1 = 6
\][/tex]
- Justification: Distributive property. This property allows us to distribute a factor (in this case, [tex]\(\frac{1}{2}\)[/tex]) to both terms inside the parentheses.
3. Step 2: Combine like terms on the left side of the equation:
[tex]\[
3x - 1 = 6
\][/tex]
- Justification: Combine like terms. We combine [tex]\(7x\)[/tex] and [tex]\(-4x\)[/tex] to get [tex]\(3x\)[/tex].
4. Step 3: Add 1 to both sides to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
3x = 7
\][/tex]
- Justification: Addition property of equality. This property allows us to add the same number (in this case, adding 1) to both sides of the equation.
5. Step 4: Divide both sides by 3 to solve for [tex]\(x\)[/tex]:
[tex]\[
x = \frac{7}{3}
\][/tex]
- Justification: Division property of equality. This property allows us to divide both sides of the equation by the same nonzero number (in this case, 3).
Putting it all together:
1. Distributive property
2. Combine like terms
3. Addition property of equality
4. Division property of equality
So, the correct sequence of justifications Kelsey used to solve this equation is:
Distributive property, Combine like terms, Addition property of equality, Division property of equality.
The correct answer is:
1. Distributive property 2 Combine like terms 3 Addition property of equality 4 Division property of equality
