To solve the inequality [tex]\(-0.06 + 7.6p < -127.74\)[/tex], follow these steps:
### Step 1: Isolate the term with the variable [tex]\(p\)[/tex]
To do this, we will add 0.06 to both sides of the inequality:
[tex]\[
-0.06 + 7.6p + 0.06 < -127.74 + 0.06
\][/tex]
Simplifying both sides, we get:
[tex]\[
7.6p < -127.68
\][/tex]
### Step 2: Solve for [tex]\(p\)[/tex]
Next, we need to isolate [tex]\(p\)[/tex] by dividing both sides of the inequality by 7.6:
[tex]\[
p < \frac{-127.68}{7.6}
\][/tex]
This simplifies to:
[tex]\[
p < -16.8
\][/tex]
### Conclusion:
The solution to the inequality is [tex]\(p < -16.8\)[/tex].
Given the options:
A. [tex]\(p < -42.6\)[/tex]
B. [tex]\(p > -16.8\)[/tex]
C. [tex]\(p < -34.57\)[/tex]
D. [tex]\(p < -16.8\)[/tex]
The correct answer is:
[tex]\[
\boxed{p < -16.8}
\][/tex]
