We want to write a negative number that has an absolute value greater than 3. Before we do that, let's recall that the absolute value of a number is the distance between the number and 0 on a number line. In other words, the absolute value of a number is the non-negative value of that number.
|a| = a and |- a| = a
This means that the absolute value of a negative number will be positive because when we evaluate the absolute value of a negative number, we erase the negative sign. Let's take a look at a number line and focus on the negative numbers.
We can see that any number less than - 3 has an absolute value greater then 3. Therefore, one example solution is - 5.
Extra
Absolute Value in the Real Life
Let's imagine that our friend lives 5 miles from the place where they sell the best ice cream in the town. However, we live on one side of the ice cream parlor and our friend lives on the opposite side of that place. We can use a number line to visualize this situation.
Here we would use the absolute value to say that we live the same distance from the ice cream parlor as our friend does because we are talking about distance and the direction does not matter.
