Let's pair the equivalent expressions by simplifying each one step-by-step:
1. Simplify the first expression:
[tex]\[
\left(4t - \frac{8}{5}\right) - \left(3 - \frac{4}{3}t\right)
\][/tex]
This expression simplifies to:
[tex]\[
5.33333333333333t - 4.6
\][/tex]
2. Simplify the second expression:
[tex]\[
7t - 22
\][/tex]
This expression simplifies to:
[tex]\[
7t - 22
\][/tex]
3. Simplify the third expression:
[tex]\[
5(2t + 1) + (-7t + 28)
\][/tex]
This expression simplifies to:
[tex]\[
3t + 33
\][/tex]
4. Simplify the fourth expression:
[tex]\[
\left(-\frac{9}{2}t + 3\right) + \left(\frac{7}{4}t + 33\right)
\][/tex]
This expression simplifies to:
[tex]\[
36 - 2.75t
\][/tex]
5. Simplify the fifth expression:
[tex]\[
-\frac{11}{4}t + 36
\][/tex]
This expression simplifies to:
[tex]\[
36 - 2.75t
\][/tex]
6. Simplify the sixth expression:
[tex]\[
\frac{16}{3}t - \frac{23}{5}
\][/tex]
This expression simplifies to:
[tex]\[
5.33333333333333t - 4.6
\][/tex]
7. Simplify the seventh expression:
[tex]\[
3(3t - 4) - (2t + 10)
\][/tex]
This expression simplifies to:
[tex]\[
7t - 22
\][/tex]
8. Simplify the eighth expression:
[tex]\[
3t + 33
\][/tex]
This expression simplifies to:
[tex]\[
3t + 33
\][/tex]
Now, let's pair the equivalent expressions:
- [tex]\(\left(4t - \frac{8}{5}\right)-\left(3-\frac{4}{3}t\right)\)[/tex] simplifies to [tex]\(5.33333333333333t - 4.6\)[/tex].
- Equivalent to [tex]\(\frac{16}{3}t - \frac{23}{5}\)[/tex], which is also [tex]\(5.33333333333333t - 4.6\)[/tex].
- [tex]\(7t - 22\)[/tex] simplifies directly to [tex]\(7t - 22\)[/tex].
- Equivalent to [tex]\(3(3t - 4) - (2t + 10)\)[/tex], which is also [tex]\(7t - 22\)[/tex].
- [tex]\(5(2t + 1) + (-7t + 28)\)[/tex] simplifies to [tex]\(3t + 33\)[/tex].
- Equivalent to [tex]\(3t + 33\)[/tex].
- [tex]\(\left(-\frac{9}{2}t + 3\right) + \left(\frac{7}{4}t + 33\right)\)[/tex] simplifies to [tex]\(36 - 2.75t\)[/tex].
- Equivalent to [tex]\(-\frac{11}{4}t + 36\)[/tex], which is also [tex]\(36 - 2.75t\)[/tex].
Thus, the correct pairs are:
1. [tex]\[
\left(4t - \frac{8}{5}\right)-\left(3-\frac{4}{3}t\right) \quad \text{with} \quad \frac{16}{3}t - \frac{23}{5}
\][/tex]
2. [tex]\[
7t - 22 \quad \text{with} \quad 3(3t - 4) - (2t + 10)
\][/tex]
3. [tex]\[
5(2t + 1) + (-7t + 28) \quad \text{with} \quad 3t + 33
\][/tex]
4. [tex]\[
\left(-\frac{9}{2}t + 3\right) + \left(\frac{7}{4}t + 33\right) \quad \text{with} \quad -\frac{11}{4}t + 36
\][/tex]
