To find the value of the expression [tex]\(\frac{x+y}{4} - \frac{9}{2z}\)[/tex] when [tex]\(x = 2\)[/tex], [tex]\(y = 4\)[/tex], and [tex]\(z = -3\)[/tex], follow these steps:
1. Substitute the values into the expression:
The given expression is:
[tex]\[
\frac{x + y}{4} - \frac{9}{2z}
\][/tex]
Substituting [tex]\(x = 2\)[/tex], [tex]\(y = 4\)[/tex], and [tex]\(z = -3\)[/tex]:
[tex]\[
\frac{2 + 4}{4} - \frac{9}{2 \times (-3)}
\][/tex]
2. Simplify the numerator and denominator separately:
- First, calculate [tex]\(x + y\)[/tex]:
[tex]\[
2 + 4 = 6
\][/tex]
- Then, calculate the denominator of the second term:
[tex]\[
2 \times (-3) = -6
\][/tex]
3. Form the simplified expression:
Substitute these results back into the expression:
[tex]\[
\frac{6}{4} - \frac{9}{-6}
\][/tex]
4. Simplify each term:
- Simplify [tex]\(\frac{6}{4}\)[/tex]:
[tex]\[
\frac{6}{4} = \frac{3}{2} = 1.5
\][/tex]
- Simplify [tex]\(\frac{9}{-6}\)[/tex]:
[tex]\[
\frac{9}{-6} = -1.5
\][/tex]
5. Combine the terms:
Now, the expression is:
[tex]\[
1.5 - (-1.5)
\][/tex]
Simplifying this:
[tex]\[
1.5 + 1.5 = 3.0
\][/tex]
Therefore, the value of the expression [tex]\(\frac{x+y}{4} - \frac{9}{2z}\)[/tex] when [tex]\(x = 2\)[/tex], [tex]\(y = 4\)[/tex], and [tex]\(z = -3\)[/tex] is [tex]\(\boxed{3.0}\)[/tex].
