Remember that the absolute value of a number describes the distance between the number and 0 on a number line.
True, see solution.
Practice makes perfect
We want to determine whether the following equality is true for x<0.
|x|=- x
We can start by recalling that the absolute value of a number is the distance between the number and 0 on a number line. First, let's consider a real life example!
Real Life Example
Let's imagine that our dog ran 3 miles away from home. We are also 3 miles from home, but in the opposite direction. We can use the number line to visualize this situation.
Here, we can use the absolute value to say that we are the same distance from home as our dog is because when we talk about distance, direction does not matter.
|3|=|-3|=3
Validity of the Statement
Recall that we want to determine whether the equality |x|=- x is true or false for x<0. We know that the absolute value of x is equal to x or - x. Let's compare |x| with the value of x and - x for a few arbitrary negative values of x!
x
- x
|x|
Is |x| Equal to - x?
- 12
- ( - 12)= 12
| - 12|= 12
Yes
- 3
- ( - 3)= 3
| - 3|= 3
Yes
- 21
- ( - 21)= 21
| - 21|= 21
Yes
We found that for negative values of x, the absolute values of x is equal to - x. This means that the given statement is true.
