Let's match each pair of equivalent expressions step-by-step:
1. Consider the first expression on the left side:
[tex]\[
(-14 + \frac{3}{2} b) - (1 + \frac{8}{2} b)
\][/tex]
This simplifies to:
[tex]\[
-14 + \frac{3}{2} b - 1 - 4b = -15 - \frac{5}{2} b
\][/tex]
Therefore, the equivalent expression is:
[tex]\[
-15 - \frac{5}{2} b
\][/tex]
2. Consider the second expression on the left side:
[tex]\[
(5 + 2b) + (2b + \frac{3}{2})
\][/tex]
This simplifies to:
[tex]\[
5 + 2b + 2b + \frac{3}{2} = 4b + 6.5
\][/tex]
Therefore, the equivalent expression is:
[tex]\[
4b + \frac{13}{2}
\][/tex]
3. Consider the third expression on the left side:
[tex]\[
(\frac{7}{2} b - 3) - (8 + 6b)
\][/tex]
This simplifies to:
[tex]\[
\frac{7}{2} b - 3 - 8 - 6b = -\frac{5}{2} b - 11
\][/tex]
Therefore, the equivalent expression is:
[tex]\[
-\frac{5}{2} b - 11
\][/tex]
4. Consider the fourth expression on the left side:
[tex]\[
(-10 + b) + (7b - 5)
\][/tex]
This simplifies to:
[tex]\[
-10 + b + 7b - 5 = 8b - 15
\][/tex]
Therefore, the equivalent expression is:
[tex]\[
8b - 15
\][/tex]
Now, let's match these pairs of equivalent expressions:
[tex]\[
\begin{array}{l}
\left(-14+\frac{3}{2} b\right)-\left(1+\frac{8}{2} b\right) \\
\left(5+2 b\right)+\left(2 b+\frac{3}{2}\right) \\
\left(\frac{7}{2} b-3\right)-(8+6 b) \\
(-10+b)+(7 b-5) \\
\end{array}
\][/tex]
[tex]\[
\begin{array}{c}
\longleftrightarrow \\
\longleftrightarrow \\
\longleftrightarrow \\
\longleftrightarrow \\
\end{array}
\][/tex]
[tex]\[
\begin{array}{r}
-15-\frac{5}{2} b \\
4 b+\frac{13}{2} \\
-\frac{5}{2} b-11 \\
8 b-15 \\
\end{array}
\][/tex]
