Let's analyze each pair of expressions to determine if they are equivalent or not equivalent:
1. Expressions: [tex]\(5x - 7 + 3x\)[/tex] and [tex]\(3x - 7 + 5x\)[/tex]
To determine if these expressions are equivalent, we simplify both:
[tex]\[
5x - 7 + 3x = (5x + 3x) - 7 = 8x - 7
\][/tex]
[tex]\[
3x - 7 + 5x = (3x + 5x) - 7 = 8x - 7
\][/tex]
Since both simplified expressions are [tex]\(8x - 7\)[/tex], these expressions are equivalent.
2. Expressions: [tex]\(4y + 9 + 3y\)[/tex] and [tex]\(3y + 9 + 4y\)[/tex]
Simplify both expressions:
[tex]\[
4y + 9 + 3y = (4y + 3y) + 9 = 7y + 9
\][/tex]
[tex]\[
3y + 9 + 4y = (3y + 4y) + 9 = 7y + 9
\][/tex]
Since both simplified expressions are [tex]\(7y + 9\)[/tex], these expressions are equivalent.
3. Expressions: [tex]\(6z - 2z + 4\)[/tex] and [tex]\(4 + 2z - 6z\)[/tex]
Simplify both expressions:
[tex]\[
6z - 2z + 4 = (6z - 2z) + 4 = 4z + 4
\][/tex]
[tex]\[
4 + 2z - 6z = 4 + (2z - 6z) = 4 - 4z
\][/tex]
Since the simplified expressions are [tex]\(4z + 4\)[/tex] and [tex]\(4 - 4z\)[/tex], these expressions are not equivalent.
Based on the above analysis:
[tex]\[
\begin{array}{|l|c|}
\hline
\text{Expressions} & \text{Equivalent or Not Equivalent?} \\
\hline
5x - 7 + 3x \text{ and } 3x - 7 + 5x & \text{equivalent} \\
\hline
4y + 9 + 3y \text{ and } 3y + 9 + 4y & \text{equivalent} \\
\hline
6z - 2z + 4 \text{ and } 4 + 2z - 6z & \text{not equivalent} \\
\hline
\end{array}
\][/tex]
