To evaluate the expression [tex]\(\frac{5|x| - y^3}{x}\)[/tex] given [tex]\(x = -5\)[/tex] and [tex]\(y = 10\)[/tex]:
1. First, calculate the absolute value of [tex]\(x\)[/tex]:
[tex]\[
|x| = |-5| = 5
\][/tex]
2. Next, multiply this absolute value by 5:
[tex]\[
5 |x| = 5 \times 5 = 25
\][/tex]
3. Now, calculate [tex]\(y^3\)[/tex]:
[tex]\[
y = 10 \implies y^3 = 10^3 = 1000
\][/tex]
4. Substitute [tex]\(5 |x|\)[/tex] and [tex]\(y^3\)[/tex] into the numerator of the expression:
[tex]\[
5 |x| - y^3 = 25 - 1000 = -975
\][/tex]
5. Finally, substitute [tex]\(x = -5\)[/tex] into the denominator and divide:
[tex]\[
\frac{5 |x| - y^3}{x} = \frac{-975}{-5} = 195
\][/tex]
Thus, the finalized value of the expression is [tex]\(195\)[/tex]. Since this value is not among the given choices (A. 3,120 B. 620 C. -3,130 D. -630), it appears there might be an error in the options provided.
Therefore, none of the given choices (A, B, C, or D) is correct based on the evaluation of this expression. The result is actually [tex]\(195\)[/tex].
