Question

Simplify. Consider all cases. |x+7|, if x > , if x = , if x <

Answer 1

Answer:

x > -7: x + 7

x = -7: 0

x < -7: -x - 7

Step-by-step explanation:

|x + 7| = x + 7

When x + 7 > 0

x > -7

|x + 7| = -(x + 7) = -x - 7

When x + 7 < 0

x < -7

|x + 7| = 0

When x + 7 = 0

x = -7

Answer 2

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!