To solve the inequality [tex]\(-3p + 6.7 > -4.4\)[/tex], we will follow these steps:
1. Isolate the term with the variable [tex]\(p\)[/tex]:
- We start by isolating [tex]\(p\)[/tex] on one side of the inequality. To do this, we need to get rid of the constant term on the left side. We will subtract 6.7 from both sides of the inequality.
[tex]\[
-3p + 6.7 - 6.7 > -4.4 - 6.7
\][/tex]
Simplifying this, we get:
[tex]\[
-3p > -11.1
\][/tex]
2. Eliminate the coefficient of [tex]\(p\)[/tex]:
- To solve for [tex]\(p\)[/tex], we need to divide both sides of the inequality by -3. It's important to remember that dividing by a negative number reverses the inequality sign.
[tex]\[
p < \frac{-11.1}{-3}
\][/tex]
Simplifying the right-hand side, we get:
[tex]\[
p < 3.7
\][/tex]
So, the solution to the inequality [tex]\(-3p + 6.7 > -4.4\)[/tex] is:
[tex]\[
p < 3.7
\][/tex]
### Graphing the Solution
To graph the solution [tex]\(p < 3.7\)[/tex], we follow these steps:
1. Draw a number line.
2. Locate the point [tex]\(3.7\)[/tex] on the number line.
3. Since [tex]\(p < 3.7\)[/tex] does not include [tex]\(3.7\)[/tex] itself, we represent this with an open circle at [tex]\(3.7\)[/tex].
4. Shade the portion of the number line to the left of [tex]\(3.7\)[/tex] to indicate all values less than [tex]\(3.7\)[/tex].
Here is the graphical representation:
```
<----|----|----|----|----|----|----|----|----|----|------>
2 2.5 3 3.5 (3.7) <---- this is open circle ----
↑
3.7
```
All the numbers less than [tex]\(3.7\)[/tex] are part of the solution set, which is represented by the shaded region extending to the left from [tex]\(3.7\)[/tex].
