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When [tex]\( x=5 \)[/tex], the value of the expression [tex]\( \frac{20}{-25 + x} - 2(x - 10) \)[/tex] is:

A. [tex]\(-21\)[/tex]
B. [tex]\(-9\)[/tex]
C. [tex]\(9\)[/tex]
D. [tex]\(19\)[/tex]

Sagot :

GinnyAnswer
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]
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