Some of my SAT students have been wrestling with absolute value lately. I think it’s giving them fits because most of them haven’t seen it in a long time.
Here’s the trick to absolute value equations. Each equation has two solutions – the positive one and the negative one. You’ll usually need to solve it both ways.
Here’s an real life example. This is question 5.4.10 from the Blue Book. [Note: This question is pulled from the old test. But the SAT is still testing absolute value on the new test.]
It could be positive OR it could be negative
The absolute value signs mean that you take whatever value is in the bar and you turn it positive.
So if |x|=3, that means that x could be either positive 3 or negative 3.
So you need to solve for both possibilities
And solve the second equation for both the positive or negative value as well.
Now, let’s go back to the problem and re-read what they are looking for.
Which value of k satisfies both equations?
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