Strategies, Sample Questions, and Random Ramblings.
July 18, 2015
GMAT absolute value, and any absolute value really, is really just a way to measure the distance from zero. And, since distances can only be positive, we can rephrase absolute value as the positive difference from 0. In reality, all you need to know at the core is that the absolute value of a number is the number itself if positive or the number times -1 if it is negative.
The absolute value of x is denoted |x| . To illustrate how this works, let’s look at examples:
While the first are probably pretty obvious, the last one my throw you a bit. The reason that the absolute value of -x does not equal x is because we do not know if x is positive or negative. In concrete terms if x were to equal -4, then the absolute value of negative -4 is not negative 4, it is 4. Be careful on making assumptions.
We can also have more complicated expressions inside absolute value signs and absolute value signs within equations.
Let’s start with a basic equation and build up.
|x| = 4
To solve this, and any other absolute value equation, we will actually solve two different equations. The first is easy; we just remove the absolute value symbol altogether. Thus,
x = 4
The second is a bit trickier. Because the term inside the absolute value symbol can also be negative (and then switch to positive via the symbol), we set the term or expression inside the absolute value symbol equal to the opposite of the other side of the equation.
x = -4
In short, x = 4 or -4 (or ± 4)
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