To evaluate the expression [tex]\(\frac{20}{-25 + x} - 2(x - 10)\)[/tex] for [tex]\(x = 5\)[/tex]:
1. Substitute [tex]\(x = 5\)[/tex] into the expression:
[tex]\[
\frac{20}{-25 + 5} - 2(5 - 10)
\][/tex]
2. Simplify inside the parentheses first:
For the denominator in the fraction:
[tex]\[
-25 + 5 = -20
\][/tex]
The expression now looks like:
[tex]\[
\frac{20}{-20} - 2(5 - 10)
\][/tex]
3. Simplify the fraction:
[tex]\[
\frac{20}{-20} = -1
\][/tex]
So the expression is now:
[tex]\[
-1 - 2(5 - 10)
\][/tex]
4. Simplify inside the parentheses for the second term:
[tex]\[
5 - 10 = -5
\][/tex]
So the expression is now:
[tex]\[
-1 - 2(-5)
\][/tex]
5. Simplify the multiplication:
[tex]\[
2(-5) = -10
\][/tex]
So the entire expression now is:
[tex]\[
-1 - (-10)
\][/tex]
6. Simplify subtraction with a negative number:
[tex]\[
-1 + 10 = 9
\][/tex]
So, the value of the expression [tex]\(\frac{20}{-25 + 5} - 2(5 - 10)\)[/tex] when [tex]\(x = 5\)[/tex] is [tex]\(9\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{9} \][/tex]
