Drag the tiles to the boxes to form correct pairs. Match the pairs of equivalent expressions.

[tex]\[ \left(-14 + \frac{3}{2} b\right) - \left(1 + \frac{8}{2} b\right) \][/tex]
[tex]\[ 4b + \frac{13}{2} \][/tex]
[tex]\[ (5 + 2b) + \left(2b + \frac{3}{2}\right) \][/tex]
[tex]\[ 8b - 15 \][/tex]
[tex]\[ \left(\frac{7}{2} b - 3\right) - (8 + 6b) \][/tex]
[tex]\[ \frac{-5}{2} b - 11 \][/tex]
[tex]\[ (-10 + b) + (7b - 5) \][/tex]
[tex]\[ -15 - \frac{5}{2} b \][/tex]

[tex]\[\quad\][/tex]
[tex]\[\longleftrightarrow\][/tex]
[tex]\[\square\][/tex]
[tex]\[\square \longleftrightarrow \square\][/tex]
[tex]\[\square\][/tex]
[tex]\[\square\][/tex]
[tex]\[\square \longleftrightarrow \square\][/tex]



Answer :

Let's match the pairs of equivalent expressions step-by-step:

Step 1: Expand and simplify the expressions on the left.

1. [tex]\(\left(-14+\frac{3}{2} b\right)-\left(1+\frac{8}{2} b\right)\)[/tex]

Simplify:
[tex]\[ -14 + \frac{3}{2}b - 1 - 4b = -15 - \frac{5}{2}b \][/tex]

2. [tex]\((5+2b)+\left(2b+\frac{3}{2}\right)\)[/tex]

Simplify:
[tex]\[ 5 + 2b + 2b + \frac{3}{2} = 4b + \frac{13}{2} \][/tex]

3. [tex]\(\left(\frac{7}{2} b-3\right)-(8+6b)\)[/tex]

Simplify:
[tex]\[ \frac{7}{2}b - 3 - 8 - 6b = \frac{7}{2}b - 6b - 3 - 8 = -\frac{5}{2}b - 11 \][/tex]

4. [tex]\((-10+b)+(7b-5)\)[/tex]

Simplify:
[tex]\[ -10 + b + 7b - 5 = 8b - 15 \][/tex]

Step 2: Identify the matching pairs based on the simplified expressions.

- [tex]\(\left(-14+\frac{3}{2} b\right)-\left(1+\frac{8}{2} b\right) \longleftrightarrow -15-\frac{5}{2}b\)[/tex]

- [tex]\((5+2b)+\left(2b+\frac{3}{2}\right) \longleftrightarrow 4b+\frac{13}{2}\)[/tex]

- [tex]\(\left(\frac{7}{2} b-3\right)-(8+6b) \longleftrightarrow -\frac{5}{2}b-11\)[/tex]

- [tex]\((-10+b)+(7b-5) \longleftrightarrow 8b-15\)[/tex]

So, the correct pairs are:

[tex]\[ \left(-14+\frac{3}{2} b\right)-\left(1+\frac{8}{2} b\right) \longleftrightarrow -15 - \frac{5}{2} b \][/tex]

[tex]\[ (5+2 b) + \left(2 b+\frac{3}{2}\right) \longleftrightarrow 4 b+\frac{13}{2} \][/tex]

[tex]\[ \left(\frac{7}{2} b-3\right)-(8+6 b) \longleftrightarrow \frac{-5}{2} b-11 \][/tex]

[tex]\[ (-10+b)+(7 b-5) \longleftrightarrow 8 b-15 \][/tex]