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.
Which value of k satisfies both equations?
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