To solve the inequality [tex]\( x \geq -7 \)[/tex], we need to identify numbers that either satisfy or exceed [tex]\(-7\)[/tex]. Here’s a step-by-step solution to find such numbers and graph the inequality on a number line.
### Step-by-Step Solution:
1. Understand the Inequality [tex]\( x \geq -7 \)[/tex]:
- The inequality [tex]\( x \geq -7 \)[/tex] means [tex]\( x \)[/tex] can be [tex]\(-7\)[/tex] or any number greater than [tex]\(-7\)[/tex].
2. Identify Three Possible Solutions:
- We need to find three different numbers that satisfy the inequality.
- One obvious solution is the boundary itself: [tex]\( -7 \)[/tex].
- Another solution could be [tex]\( 0 \)[/tex], which is greater than [tex]\(-7\)[/tex].
- A third solution could be [tex]\( 7 \)[/tex], which is also greater than [tex]\(-7\)[/tex].
- Hence, the three possible solutions are: [tex]\( -7, 0, 7 \)[/tex].
3. Graphing the Inequality on a Number Line:
- To graph [tex]\( x \geq -7 \)[/tex] on a number line, follow these steps:
- Draw a horizontal line and mark points indicating relevant numbers, including [tex]\(-7\)[/tex], [tex]\(0\)[/tex], and [tex]\(7\)[/tex].
- Place a filled circle (●) at [tex]\(-7\)[/tex] to indicate that [tex]\(-7\)[/tex] is included in the solution set.
- Draw a line extending to the right from the point [tex]\(-7\)[/tex]. This indicates all numbers greater than [tex]\(-7\)[/tex] are included.
Here’s how the graph looks:
```
←-------------●============>
-7 0 7
```
- The arrow to the right indicates that the line extends infinitely in that direction, meaning all values greater than -7.
### Conclusion:
Three possible solutions to the inequality [tex]\( x \geq -7 \)[/tex] are [tex]\( -7, 0, \)[/tex] and [tex]\( 7 \)[/tex]. The graph on the number line shows all numbers from [tex]\(-7\)[/tex] onwards (including [tex]\(-7\)[/tex]) as part of the solution set.
