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

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

[tex]\[
\begin{array}{l}
\square \longleftrightarrow \square \\
\square \longleftrightarrow \square \\
\square \longleftrightarrow \square \\
\square \longleftrightarrow \square \\
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
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]
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