To solve the equation [tex]\( \frac{17}{3}\left(x - \frac{3}{2}\right) = -\frac{5}{4} \)[/tex], we will follow these steps:
1. Distribute the fraction [tex]\(\frac{17}{3}\)[/tex] inside the parentheses:
[tex]\[
\frac{17}{3} \cdot x - \frac{17}{3} \cdot \frac{3}{2}
\][/tex]
Simplify the multiplication:
[tex]\[
\frac{17}{3} \cdot \frac{3}{2} = \frac{17 \cdot 3}{3 \cdot 2} = \frac{17}{2}
\][/tex]
So the equation becomes:
[tex]\[
\frac{17}{3}x - \frac{17}{2} = -\frac{5}{4}
\][/tex]
2. Isolate the term involving [tex]\(x\)[/tex] by adding [tex]\(\frac{17}{2}\)[/tex] to both sides:
[tex]\[
\frac{17}{3}x = -\frac{5}{4} + \frac{17}{2}
\][/tex]
To add the fractions, we need a common denominator. The common denominator for [tex]\(\frac{5}{4}\)[/tex] and [tex]\(\frac{17}{2}\)[/tex] is 4:
[tex]\[
\frac{17}{2} = \frac{17 \cdot 2}{2 \cdot 2} = \frac{34}{4}
\][/tex]
Now the equation is:
[tex]\[
\frac{17}{3}x = -\frac{5}{4} + \frac{34}{4} = \frac{34 - 5}{4} = \frac{29}{4}
\][/tex]
3. Solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(\frac{17}{3}\)[/tex]:
[tex]\[
x = \frac{\frac{29}{4}}{\frac{17}{3}} = \frac{29}{4} \cdot \frac{3}{17} = \frac{29 \cdot 3}{4 \cdot 17} = \frac{87}{68}
\][/tex]
Simplifying [tex]\(\frac{87}{68}\)[/tex], if necessary:
[tex]\[
\frac{87}{68}
\][/tex]
Since 87 and 68 have no common factors other than 1, this fraction is in simplest form.
So, the correct answer is:
[tex]\[
\boxed{\frac{87}{68}}
\][/tex]
Thus, the answer is [tex]\( \text{B. } x = \frac{87}{68} \)[/tex].
