To solve for [tex]\( x \)[/tex] in the inequality [tex]\( 0.80x - 5.00 \leq 6500 \)[/tex], let's go through the steps systematically:
1. Start with the given inequality:
[tex]\[
0.80x - 5.00 \leq 6500
\][/tex]
2. Add [tex]\( 5.00 \)[/tex] to both sides to isolate the term involving [tex]\( x \)[/tex]:
[tex]\[
0.80x - 5.00 + 5.00 \leq 6500 + 5.00
\][/tex]
Simplifying this, we get:
[tex]\[
0.80x \leq 6505
\][/tex]
3. Divide both sides of the inequality by [tex]\( 0.80 \)[/tex] to solve for [tex]\( x \)[/tex]:
[tex]\[
x \leq \frac{6505}{0.80}
\][/tex]
4. Performing the division on the right side:
[tex]\[
x \leq 8131.25
\][/tex]
So, the correct inequality representing all possible solutions for [tex]\( x \)[/tex] is:
[tex]\[
x \leq 8131.25
\][/tex]
Let's match this result with the given options.
- Option A: [tex]\(x \leq 75.00\)[/tex]
- Option B: [tex]\(x \leq 76.25\)[/tex]
- Option C: [tex]\(x \leq 86.25\)[/tex]
- Option D: [tex]\(x \leq 87.50\)[/tex]
None of these options match our result of [tex]\( x \leq 8131.25 \)[/tex]. Therefore, there must be an error in the options provided as none of them represent the correct solution. The correct inequality, as determined by the steps above, is [tex]\( x \leq 8131.25 \)[/tex].
