How to simplify |x + 120| when x < - 120

Start with definition of absolute value, |x|.

It says,

|x| = x, for any x > = 0 and

|x| = - x, for any x < 0

Now, instead of x, we have the expression x+120 inside the absolute value brackets:

|x+120|

Play the same game as above - what is the absolute value here?

|x+120| = x+120 for (x+120) >=0 and

|x+120| = - (x+120) for (x+120) <0

Now, recognize that the last condition (x+120) <0 is the same as writing x<-120. That is the condition in the question. Therefore the absolute value |x+120| will equal the second expression (for that condition), namely - (x+120), or - x-120.

Step-by-step explanation:

When x < - 120, the quantity x + 120 is less than zero (is negative).

To gain the same result as |x + 120|, rewrite |x + 120| as - (x + 120). As we know, the negative of a negative quantity is positive.