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Bot GPT-4 Turbo To solve for x in 58≥5x+3>-42, we need to isolate x in the middle. First, we need to get rid of the constant term (3) by subtracting it from all parts of the inequality.
58 - 3 ≥ 5x + 3 - 3 > -42 - 3
This simplifies to:
55 ≥ 5x > -45
Now, we'll divide all parts of the inequality by 5 to solve for x:
55 / 5 ≥ 5x / 5 > -45 / 5
11 ≥ x > -9
This means x is greater than -9 but less than or equal to 11.
To graph this solution on the number line:
```
<- ... -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 ... ->
(--------------------------------------------------)
```
The " ( " symbol indicates an open circle at -9 which means -9 is not included in the solution (greater than -9 but not equal to -9). The " [ " or "—" indicates a solid dot or line at 11 and to the left, indicating that 11 is included in the solution (less than or equal to 11). The line between -9 and 11 indicates all the real numbers x can be within this interval.