To determine the simplified form of the expression [tex]\(3\left(\frac{7}{5} x+4\right)-2\left(\frac{3}{2}-\frac{5}{4} x\right)\)[/tex], we can follow these steps:
1. Distribute the constants through each of the terms inside the parentheses.
[tex]\[
3\left(\frac{7}{5} x + 4\right) \Rightarrow 3 \cdot \frac{7}{5} x + 3 \cdot 4 = \frac{21}{5} x + 12
\][/tex]
[tex]\[
-2\left(\frac{3}{2} - \frac{5}{4} x\right) \Rightarrow -2 \cdot \frac{3}{2} + [-2 \cdot (-\frac{5}{4} x)] = -3 + \frac{10}{4} x = -3 + \frac{5}{2} x
\][/tex]
2. Combine the two simplified parts:
[tex]\[
\frac{21}{5} x + 12 - 3 + \frac{5}{2} x
\][/tex]
3. Add/Subtract the constants separately:
[tex]\[
12 - 3 = 9
\][/tex]
4. Combine the x terms:
To combine [tex]\(\frac{21}{5} x + \frac{5}{2} x\)[/tex], we need a common denominator. The common denominator for 5 and 2 is 10.
[tex]\[
\frac{21}{5} x = \frac{42}{10} x
\][/tex]
[tex]\[
\frac{5}{2} x = \frac{25}{10} x
\][/tex]
[tex]\[
\frac{42}{10} x + \frac{25}{10} x = \frac{67}{10} x
\][/tex]
So, the expression simplifies to:
[tex]\[
\frac{67}{10} x + 9
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{67}{10} x + 9}
\][/tex]
Upon review of the given options, we find that option B matches the simplified expression:
Option B: [tex]\(\frac{67}{10} x + 9\)[/tex]
So, the correct choice is:
B. [tex]\(\frac{67}{10} x+9\)[/tex]
