Answered

Dive into the world of knowledge and get your queries resolved at IDNLearn.com. Find the information you need quickly and easily with our comprehensive and accurate Q&A platform.

The solution process is shown for an equation. Justify each step in the process with the appropriate property. Select the correct answer from each drop-down menu.

\begin{tabular}{|c|c|}
\hline
[tex]$2(3y + 4) - 3(y - 2) = 2y$[/tex] & original equation \\
\hline
[tex]$6y + 8 - 3y + 6 = 2y$[/tex] & distributive property \\
\hline
[tex]$3y + 14 = 2y$[/tex] & combining like terms \\
\hline
[tex]$14 = -y$[/tex] & subtraction property of equality \\
\hline
[tex]$-14 = y$[/tex] & multiplication property of equality \\
\hline
[tex]$y = -14$[/tex] & symmetric property of equality \\
\hline
\end{tabular}

Sagot :

GinnyAnsweridn
Sure, let's go through the steps one by one, justifying each step with the appropriate property.

1. Original Equation
[tex]\[ 2(3y + 4) - 3(y - 2) = 2y \][/tex]

2. Distribute
[tex]\[ 6y + 8 - 3y + 6 = 2y \][/tex]
In this step, we used the Distributive Property. This property states that [tex]\(a(b + c) = ab + ac\)[/tex]. So we distribute the multiplication over addition and subtraction inside the parentheses.

3. Combine Like Terms
[tex]\[ 3y + 14 = 2y \][/tex]
Here, we combined like terms. The terms involving [tex]\(y\)[/tex] are [tex]\(6y\)[/tex] and [tex]\(-3y\)[/tex], which combine to [tex]\(3y\)[/tex]. The constant terms [tex]\(8\)[/tex] and [tex]\(6\)[/tex] combine to give [tex]\(14\)[/tex].

4. Isolate Variable Terms on One Side
[tex]\[ 14 = 2y - 3y \][/tex]
We employed the Subtraction Property of Equality, which allows us to subtract the same amount from both sides of an equation. Here, it helps us move the variable term [tex]\(3y\)[/tex] to the other side by subtracting [tex]\(3y\)[/tex] from both sides. This simplifies the equation.

5. Combine Like Terms Again
[tex]\[ 14 = -y \][/tex]
Here, we combine the like terms [tex]\(2y - 3y\)[/tex] to get [tex]\(-y\)[/tex]. This step is another application of combining like terms.

6. Isolate the Variable
[tex]\[ -14 = y \][/tex]
Finally, we use the Multiplication Property of Equality, specifically multiplying both sides by -1, to solve for [tex]\(y\)[/tex].

7. Solution
[tex]\[ y = -14 \][/tex]
Thus, we isolate [tex]\(y\)[/tex] and find the solution to be [tex]\(y = -14\)[/tex].

Putting it all together in the correct order:
1. Original Equation: [tex]\(2(3y + 4) - 3(y - 2) = 2y\)[/tex]
2. Distribute: [tex]\(6y + 8 - 3y + 6 = 2y\)[/tex]
3. Combine Like Terms: [tex]\(3y + 14 = 2y\)[/tex]
4. Subtraction Property of Equality: [tex]\(14 = 2y - 3y\)[/tex]
5. Combine Like Terms: [tex]\(14 = -y\)[/tex]
6. Multiplication Property of Equality: [tex]\(-14 = y\)[/tex]
7. Solution: [tex]\(y = -14\)[/tex]

Each step uses appropriate properties to transform the equation into a simpler form until we isolate [tex]\(y\)[/tex].
We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Your search for solutions ends at IDNLearn.com. Thank you for visiting, and we look forward to helping you again.