To solve the equation for [tex]\(x\)[/tex]:
[tex]\[
\frac{x+5}{2}=\frac{38}{16}
\][/tex]
First, we simplify the right-hand side of the equation:
[tex]\[
\frac{38}{16} = 2.375
\][/tex]
So the equation becomes:
[tex]\[
\frac{x+5}{2} = 2.375
\][/tex]
Next, we want to isolate [tex]\(x\)[/tex]. To do that, we first get rid of the denominator 2 by multiplying both sides of the equation by 2:
[tex]\[
x + 5 = 2 \times 2.375
\][/tex]
Calculate [tex]\(2 \times 2.375\)[/tex]:
[tex]\[
2 \times 2.375 = 4.75
\][/tex]
Thus, the equation now is:
[tex]\[
x + 5 = 4.75
\][/tex]
To solve for [tex]\(x\)[/tex], subtract 5 from both sides:
[tex]\[
x = 4.75 - 5
\][/tex]
This simplifies to:
[tex]\[
x = -0.25
\][/tex]
So, the solution set is:
[tex]\[
\{x \mid x = -0.25\}
\][/tex]
Therefore, the correct choice is:
A. The solution set is [tex]\(\{-0.25\}\)[/tex].
