To find 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 break this down into smaller steps.
First, distribute the constants inside each parenthesis:
1. [tex]\( 3\left(\frac{7}{5} x + 4\right) \)[/tex]:
[tex]\[
3 \cdot \frac{7}{5} x + 3 \cdot 4 = \frac{21}{5} x + 12
\][/tex]
2. [tex]\( 2\left(\frac{3}{2} - \frac{5}{4} x\right) \)[/tex]:
[tex]\[
2 \cdot \frac{3}{2} - 2 \cdot \frac{5}{4} x = 3 - \frac{10}{4} x = 3 - \frac{5}{2} x
\][/tex]
Now, substitute these back into the original expression:
[tex]\[
\left(\frac{21}{5} x + 12\right) - \left(3 - \frac{5}{2} x\right)
\][/tex]
Next, distribute the negative sign and simplify:
[tex]\[
\frac{21}{5} x + 12 - 3 + \frac{5}{2} x
\][/tex]
Combine like terms:
[tex]\[
\left(\frac{21}{5} x + \frac{5}{2} x\right) + (12 - 3)
\][/tex]
First, find a common denominator for the x terms:
- [tex]\(\frac{21}{5} x = \frac{42}{10} x\)[/tex]
- [tex]\(\frac{5}{2} x = \frac{25}{10} x\)[/tex]
Add these:
[tex]\[
\frac{42}{10} x + \frac{25}{10} x = \frac{67}{10} x
\][/tex]
Combine the constants:
[tex]\[
12 - 3 = 9
\][/tex]
So, the simplified form of the expression is:
[tex]\[
\frac{67}{10} x + 9
\][/tex]
Thus, the correct answer is [tex]\( \boxed{\frac{67}{10} x + 9} \)[/tex]. This corresponds to option B.
