Great question! To evaluate the expression [tex]\(\frac{12-3v}{2} + \left(\frac{2v-4}{v}\right)\)[/tex] for [tex]\(v = 3\)[/tex], we will follow a step-by-step approach:
1. Substitute [tex]\(v = 3\)[/tex] into the expression:
The expression is:
[tex]\[
\frac{12 - 3v}{2} + \left(\frac{2v - 4}{v}\right)
\][/tex]
Substituting [tex]\(v = 3\)[/tex]:
[tex]\[
\frac{12 - 3 \cdot 3}{2} + \left(\frac{2 \cdot 3 - 4}{3}\right)
\][/tex]
2. Evaluate the first part of the expression [tex]\(\frac{12 - 3 \cdot 3}{2}\)[/tex]:
- Calculate [tex]\(3 \cdot 3\)[/tex]:
[tex]\[
3 \cdot 3 = 9
\][/tex]
- Subtract this from 12:
[tex]\[
12 - 9 = 3
\][/tex]
- Divide by 2:
[tex]\[
\frac{3}{2} = 1.5
\][/tex]
3. Evaluate the second part of the expression [tex]\(\left(\frac{2 \cdot 3 - 4}{3}\right)\)[/tex]:
- Calculate [tex]\(2 \cdot 3\)[/tex]:
[tex]\[
2 \cdot 3 = 6
\][/tex]
- Subtract 4 from this:
[tex]\[
6 - 4 = 2
\][/tex]
- Divide by 3:
[tex]\[
\frac{2}{3} \approx 0.6666666666666666
\][/tex]
4. Add the results from both parts:
- Add [tex]\(1.5\)[/tex] and [tex]\(0.6666666666666666\)[/tex]:
[tex]\[
1.5 + 0.6666666666666666 \approx 2.1666666666666665
\][/tex]
So, after evaluating the expression step-by-step for [tex]\(v = 3\)[/tex], the result is approximately:
[tex]\[
2.1666666666666665
\][/tex]
