Answer and Step-by-step explanation:
There are 3 cases we need to consider:
1. x > -7
2. x = -7
3. x < -7
Case 1: x > -7
If x is greater than -7, then we know that any number x + 7 will be a positive number. This is because -7 is the smallest negative number possible that will produce a non-positive number; any number greater than -7 will give a positive number in x + 7. So, the simplified expression of |x + 7| is just x + 7.
Case 2: x = -7
If x = -7, we know that -7 + 7 = 0, so |x + 7| when x = -7 is simply 0.
Case 3: x < -7
If x is less than -7, then from the argument in Case 1, we know that all numbers x + 7 will be negative. This means that when simplifying the absolute value expression, we have to switch the two terms. So, the simplified expression of |x + 7| when x < -7 is 7 + x. (Note that this isn't the same as x + 7 because here, x is always a negative number)
Hope this helps!