To solve the given equation [tex]\(4x + \frac{1}{2}(10x - 4) = 6\)[/tex] step by step, we follow the procedure outlined below:
1. Distributive Property: First, we distribute [tex]\(\frac{1}{2}\)[/tex] across the terms inside the parentheses.
[tex]\[
4x + \frac{1}{2}(10x) - \frac{1}{2}(4) = 6 \implies 4x + 5x - 2 = 6
\][/tex]
2. Combine like terms: Next, we combine the terms involving [tex]\(x\)[/tex].
[tex]\[
4x + 5x - 2 = 6 \implies 9x - 2 = 6
\][/tex]
3. Addition Property of Equality: To isolate the term involving [tex]\(x\)[/tex], we add 2 to both sides of the equation.
[tex]\[
9x - 2 + 2 = 6 + 2 \implies 9x = 8
\][/tex]
4. Division Property of Equality: Finally, to solve for [tex]\(x\)[/tex], we divide both sides by 9.
[tex]\[
9x / 9 = 8 / 9 \implies x = \frac{8}{9}
\][/tex]
With these steps and the corresponding justifications, the correct set of justifications that Bruno used to solve this equation is:
c. 1. Distributive Property
2. Combine like terms
3. Addition Property of Equality
4. Division Property of Equality
Thus, the correct answer is:
c
