Sure, let's match the pairs of equivalent expressions by pairing each given expression with its simplified form.
1. [tex]\(\left(-14 + \frac{3}{2} b\right) - \left(1 + \frac{8}{2} b\right)\)[/tex]
Simplified form: [tex]\(-2.5b - 15\)[/tex]
2. [tex]\(4b + \frac{13}{2}\)[/tex]
Simplified form: [tex]\(4b + 6.5\)[/tex]
3. [tex]\((5 + 2b) + \left(2b + \frac{3}{2}\right)\)[/tex]
Simplified form: [tex]\(4b + 6.5\)[/tex]
4. [tex]\(8b - 15\)[/tex]
Simplified form: [tex]\(8b - 15\)[/tex]
5. [tex]\(\left(\frac{7}{2}b - 3\right) - (8 + 6b)\)[/tex]
Simplified form: [tex]\(-2.5b - 11\)[/tex]
6. [tex]\(\frac{-5}{2}b - 11\)[/tex]
Simplified form: [tex]\(-2.5b - 11\)[/tex]
7. [tex]\((-10 + b) + (7b - 5)\)[/tex]
Simplified form: [tex]\(8b - 15\)[/tex]
8. [tex]\(-15 - \frac{5}{2}b\)[/tex]
Simplified form: [tex]\(-2.5b - 15\)[/tex]
Now, matching the pairs of equivalent expressions, we get:
- [tex]\( \left(-14 + \frac{3}{2} b\right) - \left(1 + \frac{8}{2} b\right) \longleftrightarrow -2.5b - 15 \)[/tex]
- [tex]\( 4b + \frac{13}{2} \longleftrightarrow 4b + 6.5 \)[/tex]
- [tex]\( (5 + 2b) + \left(2b + \frac{3}{2}\right) \longleftrightarrow 4b + 6.5 \)[/tex]
- [tex]\( 8b - 15 \longleftrightarrow 8b - 15 \)[/tex]
- [tex]\( \left(\frac{7}{2}b - 3\right) - (8 + 6b) \longleftrightarrow -2.5b - 11 \)[/tex]
- [tex]\( \frac{-5}{2}b - 11 \longleftrightarrow -2.5b - 11 \)[/tex]
- [tex]\( (-10 + b) + (7b - 5) \longleftrightarrow 8b - 15 \)[/tex]
- [tex]\( -15 - \frac{5}{2}b \longleftrightarrow -2.5b - 15 \)[/tex]
