The concept of absolute value has stumped many test takers over the years. For many students, absolute value is nothing but a positive version of any number. For instance, the absolute value of 3 is 3 and -3 is also 3. While this example is correct, it is better to understand the real definition of absolute value. Absolute value of a number is the distance from zero on the number line. So, in the above example both the numbers are 3 units away from 0 on the number line.
Let’s look at two absolute value rules which will help you on the exam day.
Consider the absolute value equations as two separate equations:
Suppose you are faced with the question – What could be the value of x if
|3x-5| = 10
The two separate equations that can come out of it are:
Essentially, you are keeping one equation as it is, while the other one is multiplied by -1.
Be careful with inequalities:
Inequalities present a different challenge with absolute values and the duo often appears together in exams.
So if you have an inequality x<3, it means that all the values below 2, 1, 0, -1, -2, -3, -4…satisfy the condition.
However, if the statement is |x|<3, then the case becomes quite different. In this case, while the numbers 2, 1, 0,-1 and -2 will satisfy the condition but -4 will not since the absolute value of -4 becomes 4.
So, if you split the above inequality into two possibilities, you have
x<3 and x>-3
In the exam, be careful to read the question very carefully. Check the positive and negative, split the equation/inequality and then eliminate the value which does not match the answer choices.