Let's match the given expressions with their equivalent simplified forms step by step.
1. Given expression: [tex]\((4 t - \frac{8}{5}) - (3 - \frac{4}{3} t)\)[/tex]
- Simplified form: [tex]\(\frac{16}{3} t - \frac{23}{5}\)[/tex]
2. Given expression: [tex]\(3(3 t - 4) - (2 t + 10)\)[/tex]
- Simplified form: [tex]\(7t - 22\)[/tex]
3. Given expression: [tex]\(\left(-\frac{9}{2} t + 3\right) + \left(\frac{7}{4} t + 33\right)\)[/tex]
- Simplified form: [tex]\(36 - \frac{11}{4} t\)[/tex]
4. Given expression: [tex]\(5(2 t + 1) + (-7 t + 28)\)[/tex]
- Simplified form: [tex]\(3t + 33\)[/tex]
So, the correct pairs of equivalent expressions are:
[tex]\((4 t - \frac{8}{5}) - (3 - \frac{4}{3} t) \longleftrightarrow \frac{16}{3} t - \frac{23}{5}\)[/tex]
[tex]\(3(3 t - 4) - (2 t + 10) \longleftrightarrow 7t - 22\)[/tex]
[tex]\(\left(-\frac{9}{2} t + 3\right) + \left(\frac{7}{4} t + 33\right) \longleftrightarrow 36 - \frac{11}{4} t\)[/tex]
[tex]\(5(2 t + 1) + (-7 t + 28) \longleftrightarrow 3t + 33\)[/tex]
Below is the aligned solution in form of matching boxes:
[tex]\[
\begin{array}{c}
\left(4 t-\frac{8}{5}\right) - \left(3 -\frac{4}{3} t\right) \\
\xrightarrow{\longleftrightarrow} \\
\frac{16}{3} t - \frac{23}{5}
\end{array}
\][/tex]
[tex]\[
\begin{array}{c}
3(3 t - 4) - (2 t + 10) \\
\xrightarrow{\longleftrightarrow} \\
7t - 22
\end{array}
\][/tex]
[tex]\[
\begin{array}{c}
\left(-\frac{9}{2} t + 3\right) + \left(\frac{7}{4} t + 33\right) \\
\xrightarrow{\longleftrightarrow} \\
36 - \frac{11}{4} t
\end{array}
\][/tex]
[tex]\[
\begin{array}{c}
5(2 t + 1) + (-7 t + 28) \\
\xrightarrow{\longleftrightarrow} \\
3 t + 33
\end{array}
\][/tex]
