Okay, let's match the pairs of equivalent expressions step-by-step:
1. Expression: \((-14 + \frac{3}{2} b) - (1 + \frac{8}{2} b)\)
- Simplify the expression:
[tex]\[
(-14 + \frac{3}{2} b) - (1 + \frac{8}{2} b)
\][/tex]
[tex]\[
= -14 + \frac{3}{2} b - 1 - 4 b
\][/tex]
[tex]\[
= -15 + \left(\frac{3}{2} - 4\right)b
\][/tex]
[tex]\[
= -15 - \frac{5}{2} b
\][/tex]
- Hence, the pair is: \((-14 + \frac{3}{2} b) - (1 + \frac{8}{2} b)\) and \(-15 - \frac{5}{2} b\).
2. Expression: \((5 + 2 b) + (2 b + \frac{3}{2})\)
- Simplify the expression:
[tex]\[
(5 + 2 b) + (2 b + \frac{3}{2})
\][/tex]
[tex]\[
= 5 + 2b + 2b + \frac{3}{2}
\][/tex]
[tex]\[
= 5 + \frac{3}{2} + 4b
\][/tex]
[tex]\[
= \frac{10}{2} + \frac{3}{2} + 4b
\][/tex]
[tex]\[
= \frac{13}{2} + 4b
\][/tex]
- Hence, the pair is: \((5 + 2 b) + (2 b + \frac{3}{2})\) and \(4 b + \frac{13}{2}\).
3. Expression: \(\left(\frac{7}{2} b - 3\right) - (8 + 6 b)\)
- Simplify the expression:
[tex]\[
\left(\frac{7}{2} b - 3\right) - (8 + 6 b)
\][/tex]
[tex]\[
= \frac{7}{2} b - 3 - 8 - 6 b
\][/tex]
[tex]\[
= -3 - 8 + \left(\frac{7}{2} - 6\right) b
\][/tex]
[tex]\[
= -11 - \frac{5}{2} b
\][/tex]
- Hence, the pair is: \((\frac{7}{2} b - 3) - (8 + 6 b)\) and \(-11 - \frac{5}{2} b\).
4. Expression: \((-10 + b) + (7 b - 5)\)
- Simplify the expression:
[tex]\[
(-10 + b) + (7 b - 5)
\][/tex]
[tex]\[
= -10 + b + 7b - 5
\][/tex]
[tex]\[
= -10 - 5 + 8b
\][/tex]
[tex]\[
= -15 + 8b
\][/tex]
- Hence, the pair is: \((-10 + b) + (7 b - 5)\) and \(8 b - 15\).
Therefore, the correct pairs are:
1. \((-14 + \frac{3}{2} b) - (1 + \frac{8}{2} b)\) and \(-15 - \frac{5}{2} b\).
2. \((5 + 2 b) + (2 b + \frac{3}{2})\) and \(4 b + \frac{13}{2}\).
3. \((\frac{7}{2} b - 3) - (8 + 6 b)\) and \(-11 - \frac{5}{2} b\).
4. [tex]\((-10 + b) + (7 b - 5)\)[/tex] and [tex]\(8 b - 15\)[/tex].
