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To solve the inequality `x + 5 ≥ 10`, we need to isolate the variable x.
First, we subtract 5 from both sides of the inequality:
x + 5 - 5 ≥ 10 - 5
x ≥ 5
Therefore, the solution to the inequality is x ≥ 5.
To graph this inequality on a number line, we start at 5 and shade all the values to the right of 5 (including 5) since x is greater than or equal to 5.
Here is the graph:
```
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
| | | | | | √ | √ | √ | √ | √ | √ | √ | √ | √ | √ | √
```
The shaded region starts from 5 and includes all the numbers to the right of 5, including 5 itself.