To simplify the given expression [tex]\(3\left(\frac{7}{5} x+4\right)-2\left(\frac{3}{2}-\frac{5}{4} x\right)\)[/tex], let's go through it step by step.
1. Distribute the constants [tex]\(3\)[/tex] and [tex]\(2\)[/tex]:
[tex]\[
3\left(\frac{7}{5} x+4\right) = 3 \cdot \frac{7}{5} x + 3 \cdot 4 = \frac{21}{5} x + 12
\][/tex]
[tex]\[
2\left(\frac{3}{2}-\frac{5}{4} x\right) = 2 \cdot \frac{3}{2} - 2 \cdot \frac{5}{4} x = 3 - \frac{10}{4} x = 3 - \frac{5}{2} x
\][/tex]
2. Rewrite and combine the terms:
Our expression now is:
[tex]\[
\left(\frac{21}{5} x + 12\right) - \left(3 - \frac{5}{2} x\right)
\][/tex]
3. Distribute the negative sign:
[tex]\[
\frac{21}{5} x + 12 - 3 + \frac{5}{2} x
\][/tex]
4. Combine the like terms (terms involving [tex]\(x\)[/tex] together and constant terms together):
For [tex]\(x\)[/tex]-terms:
[tex]\[
\frac{21}{5} x + \frac{5}{2} x
\][/tex]
To combine these, convert them to a common denominator:
[tex]\[
\frac{21}{5} x = \frac{42}{10} x, \quad \frac{5}{2} x = \frac{25}{10} x
\][/tex]
Now add them:
[tex]\[
\frac{42}{10} x + \frac{25}{10} x = \frac{67}{10} x
\][/tex]
For constant terms:
[tex]\[
12 - 3 = 9
\][/tex]
5. Put the simplified terms together:
The simplified form of the expression is:
[tex]\[
\frac{67}{10} x + 9
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{\frac{67}{10} x+9}
\][/tex]
Thus, the correct choice is:
[tex]\[
B. \frac{67}{10} x+9
\][/tex]
