Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Match the pairs of equivalent expressions.

[tex]\[
\begin{array}{ccc}
1. \left(4t - \frac{8}{5}\right) - \left(3 - \frac{4}{3}t\right) & A. 7t - 22 & B. 5(2t + 1) + (-7t + 28) \\
2. \frac{16}{3}t - \frac{23}{5} & C. \left(-\frac{9}{2}t + 3\right) + \left(\frac{7}{4}t + 33\right) & D. -\frac{11}{4}t + 36 \\
3. 3(3t - 4) - (2t + 10) & E. 3t + 33 \\
\end{array}
\][/tex]

Match each numbered expression on the left with its corresponding lettered expression on the right.

Sagot :

GinnyAnswer
To match the pairs of equivalent expressions, we need to simplify each of the given combinations step by step:

1. Simplify the expression:
[tex]\[ \left(4t - \frac{8}{5}\right) - \left(3 - \frac{4}{3} t\right) \][/tex]

First, distribute the negative sign inside the parenthesis:
[tex]\[ 4t - \frac{8}{5} - 3 + \frac{4}{3} t \][/tex]

Combine like terms:
[tex]\[ 4t + \frac{4}{3}t - \frac{8}{5} - 3 \][/tex]

To combine \(4t + \frac{4}{3}t\), find a common denominator:
[tex]\[ 4t = \frac{12}{3}t \implies \frac{12}{3}t + \frac{4}{3}t = \frac{16}{3}t \][/tex]

So, the expression simplifies to:
[tex]\[ \frac{16}{3}t - \frac{8}{5} - 3 \][/tex]

Convert -3 to a fraction with the same denominator as \(\frac{8}{5}\):
[tex]\[ -3 = -\frac{15}{5} \][/tex]

Combine \(\frac{8}{5} + \frac{15}{5}\):
[tex]\[ \frac{16}{3}t - \left(\frac{8}{5} + \frac{15}{5}\right) = \frac{16}{3}t - \frac{23}{5} \][/tex]

So, \(\left(4 t-\frac{8}{5}\right)-\left(3-\frac{4}{3} t\right)\) matches \(\frac{16}{3} t-\frac{23}{5}\).

2. Simplify the expression:
[tex]\[ 3(3t - 4) - (2t + 10) \][/tex]

First, distribute the 3:
[tex]\[ 9t - 12 - 2t - 10 \][/tex]

Combine like terms:
[tex]\[ (9t - 2t) - (12 + 10) = 7t - 22 \][/tex]

So, \(3(3 t-4)-(2 t+10)\) matches \(7 t-22\).

3. Simplify the expression:
[tex]\[ 5(2t + 1) + (-7t + 28) \][/tex]

First, distribute the 5:
[tex]\[ 10t + 5 + (-7t + 28) \][/tex]

Combine like terms:
[tex]\[ (10t - 7t) + (5 + 28) = 3t + 33 \][/tex]

So, \(5(2 t+1)+(-7 t+28)\) matches \(3 t+33\).

4. Simplify the expression:
[tex]\[ \left(-\frac{9}{2} t+3\right) + \left(\frac{7}{4} t+33\right) \][/tex]

First, find a common denominator for the terms involving \(t\):
[tex]\[ -\frac{9}{2} t = -\frac{18}{4} t \implies -\frac{18}{4} t + \frac{7}{4} t = -\frac{11}{4} t \][/tex]

Combine constant terms:
[tex]\[ 3 + 33 = 36 \][/tex]

So, \(\left(-\frac{9}{2} t+3\right)+\left(\frac{7}{4} t+33\right)\) matches \(-\frac{11}{4} t+36\).

Thus, the pairs of equivalent expressions are:

[tex]\[ \begin{array}{ccc} \left(4 t-\frac{8}{5}\right)-\left(3-\frac{4}{3} t\right) & \text{matches} & \frac{16}{3} t-\frac{23}{5} \\ 3(3 t-4)-(2 t+10) & \text{matches} & 7 t-22 \\ 5(2 t+1)+(-7 t+28) & \text{matches} & 3 t+33 \\ \left(-\frac{9}{2} t+3\right)+\left(\frac{7}{4} t+33\right) & \text{matches} & -\frac{11}{4} t+36 \\ \end{array} \][/tex]
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.