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Match the equivalent expressions.

[tex]\[
\begin{array}{l}
1. \quad 4y + 3y + 3x - 6y - 10 - 2 \\
2. \quad 5 + 2y + 7x - 4x + 3y - 17 \\
3. \quad x + 3y + 2x - 3x + 7 + 5 \\
4. \quad 3x + 2y - 2x + y + 12 \\
\end{array}
\][/tex]

[tex]\[
\begin{array}{l}
A. \quad 12 - 3y - 2x + x + 2x \\
B. \quad x - 3y + 12 \\
C. \quad x + 3y + 12 \\
D. \quad 3x + y - 12 \\
\end{array}
\][/tex]

Match each expression in the first group with its equivalent in the second group.



Answer :

GinnyAnswer
Let's match each of the given expressions with its equivalent simplified form step by step.

Expressions to simplify:
1. [tex]\(4y + 3y + 3x - 6y - 10 - 2\)[/tex]
2. [tex]\(5 + 2y + 7x - 4x + 3y - 17\)[/tex]
3. [tex]\(x + 3y + 2x - 3x + 7 + 5\)[/tex]
4. [tex]\(3x + 2y - 2x + y + 12\)[/tex]

Simplified expressions:
5. [tex]\(12 - 3y - 2x + x + 2x\)[/tex]
6. [tex]\(x - 3y + 12\)[/tex]
7. [tex]\(x + 3y + 12\)[/tex]
8. [tex]\(3x + y - 12\)[/tex]

---

### Step 1: Simplify each expression

1. [tex]\( 4y + 3y + 3x - 6y - 10 - 2 \)[/tex]
[tex]\[ = 4y + 3y - 6y + 3x - 10 - 2 \][/tex]
[tex]\[ = (4 + 3 - 6)y + 3x - 12 \][/tex]
[tex]\[ = y + 3x - 12 \][/tex]
Equivalent simplified form: [tex]\( 3x + y - 12 \)[/tex]

2. [tex]\( 5 + 2y + 7x - 4x + 3y - 17 \)[/tex]
[tex]\[ = 2y + 3y + 7x - 4x + 5 - 17 \][/tex]
[tex]\[ = (2 + 3)y + (7 - 4)x + (5 - 17) \][/tex]
[tex]\[ = 5y + 3x - 12 \][/tex]
Equivalent simplified form: [tex]\( 3x + 5y - 12 \)[/tex]

3. [tex]\( x + 3y + 2x - 3x + 7 + 5 \)[/tex]
[tex]\[ = (1 + 2 - 3)x + 3y + 7 + 5 \][/tex]
[tex]\[ = 0x + 3y + 12 \][/tex]
[tex]\[ = 3y + 12 \][/tex]
Equivalent simplified form: [tex]\( 3y + 12 \)[/tex]

4. [tex]\( 3x + 2y - 2x + y + 12 \)[/tex]
[tex]\[ = (3 - 2)x + (2 + 1)y + 12 \][/tex]
[tex]\[ = x + 3y + 12 \][/tex]
Equivalent simplified form: [tex]\( x + 3y + 12 \)[/tex]

### Step 2: Simplify each expression given for comparison

5. [tex]\( 12 - 3y - 2x + x + 2x \)[/tex]
[tex]\[ = 12 - 3y - 2x + x + 2x \][/tex]
[tex]\[ = 12 - 3y + x \][/tex]
Equivalent simplified form: [tex]\( x - 3y + 12 \)[/tex]

6. [tex]\( x - 3y + 12 \)[/tex]
Equivalent simplified form: [tex]\( x - 3y + 12 \)[/tex]

7. [tex]\( x + 3y + 12 \)[/tex]
Equivalent simplified form: [tex]\( x + 3y + 12 \)[/tex]

8. [tex]\( 3x + y - 12 \)[/tex]
Equivalent simplified form: [tex]\( 3x + y - 12 \)[/tex]

### Final Matching:
1. [tex]\(4y + 3y + 3x - 6y - 10 - 2\)[/tex] matches with [tex]\(3x + y - 12\)[/tex]
2. [tex]\(5 + 2y + 7x - 4x + 3y - 17\)[/tex] matches with [tex]\(3x + 5y - 12\)[/tex]
3. [tex]\(x + 3y + 2x - 3x + 7 + 5\)[/tex] matches with [tex]\(3y + 12\)[/tex]
4. [tex]\(3x + 2y - 2x + y + 12\)[/tex] matches with [tex]\(x + 3y + 12\)[/tex]

And for the remaining simplified expressions:
5. [tex]\(12 - 3y - 2x + x + 2x\)[/tex] matches with [tex]\(x - 3y + 12\)[/tex]
6. [tex]\(x - 3y + 12\)[/tex] matches with [tex]\(x - 3y + 12\)[/tex]
7. [tex]\(x + 3y + 12\)[/tex] matches with [tex]\(x + 3y + 12\)[/tex]
8. [tex]\(3x + y - 12\)[/tex] matches with [tex]\(3x + y - 12\)[/tex]

So the final match is:
[tex]\[ \begin{array}{c|c} \text{Original Expression} & \text{Simplified Expression} \\ \hline 4y + 3y + 3x - 6y - 10 - 2 & 3x + y - 12 \\ 5 + 2y + 7x - 4x + 3y - 17 & 3x + 5y - 12 \\ x + 3y + 2x - 3x + 7 + 5 & 3y + 12 \\ 3x + 2y - 2x + y + 12 & x + 3y + 12 \\ 12 - 3y - 2x + x + 2x & x - 3y + 12 \\ x - 3y + 12 & x - 3y + 12 \\ x + 3y + 12 & x + 3y + 12 \\ 3x + y - 12 & 3x + y - 12 \\ \end{array} \][/tex]

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