Let's solve the inequality [tex]\(2x + 5 > -9\)[/tex] step-by-step and then graph it.
### Step-by-Step Solution
1. Isolate the variable `x`:
To solve for [tex]\(x\)[/tex], we need to isolate it on one side of the inequality. Start by subtracting 5 from both sides:
[tex]\[
2x + 5 - 5 > -9 - 5
\][/tex]
Simplifying this, we get:
[tex]\[
2x > -14
\][/tex]
2. Solve for `x`:
Next, divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{2x}{2} > \frac{-14}{2}
\][/tex]
Simplifying this, we obtain:
[tex]\[
x > -7
\][/tex]
### Graphing the Solution
Now that we have the solution [tex]\(x > -7\)[/tex], we will graph this inequality.
#### Graphing Steps
1. Draw the coordinate plane:
- Label the x-axis (horizontal) and the y-axis (vertical).
2. Plot the boundary:
- Mark the line [tex]\(x = -7\)[/tex] on the x-axis. This line is the boundary for our inequality.
3. Shade the region:
- Since the inequality is [tex]\(x > -7\)[/tex], we will shade the region to the right of the line [tex]\(x = -7\)[/tex]. This indicates all [tex]\(x\)[/tex] values greater than [tex]\(-7\)[/tex].
4. Style the boundary line:
- Because the inequality is strictly greater than ([tex]\(>\)[/tex]), we use a dashed line to indicate that points on the line [tex]\(x = -7\)[/tex] are not included in the solution.
#### Graph Description
- The x-axis should be labeled with appropriate values, including -7.
- A dashed vertical line should be drawn at [tex]\(x = -7\)[/tex] to indicate the boundary.
- The region to the right of this line should be shaded to represent [tex]\(x > -7\)[/tex].
Here's a sketch of what the graph would look like:
```markdown
y
|
|
|
|
|
-------------|-----------------------
-7 x
(Region to the right of x = -7 is shaded)
```
### Conclusion
The solution to the inequality [tex]\(2x + 5 > -9\)[/tex] is [tex]\(x > -7\)[/tex]. The corresponding graph includes a dashed vertical line at [tex]\(x = -7\)[/tex] with the region to the right of this line shaded to indicate all [tex]\(x\)[/tex] values greater than [tex]\(-7\)[/tex].
