# SAT Algebra: Absolute Value

## SAT Question of the Day

The SAT question of the day is a math question that tests your ability to understand absolute value.

Start by reading the question carefully.  It looks complex because there are multiple variables, but if you paraphrase the problem you will see that it is very simple.  It costs a certain amount (d) for Alan to ship a package, as long as it is within a certain weight (p).  You know that the package is within that weight because it costs that amount.  If you know that the inequality that you are given is true, which of these other inequalities must be true?

Read the inequality in your problem as, "p is greater than or equal to 6 and less than or equal to 10."   There are many different ways that you could rearrange this inequality, so for this problem it makes sense to look at the answer choices.

When you look at your answer choices, notice that A, B, and C all compare p to negative and positive 2 (those absolute value bars tell you that whatever is inside could be negative or positive).  Your Knowsys Strategies tell you that the test makers often try to hide the answer by providing answers that are similar to the correct answer.  Your answer is probably among these choices, but even if it is not, you can eliminate all three if you compare p to positive and negative 2 and your answer does not match these choices.

6 ≤ p ≤ 10

You want to compare p to positive and negative 2.   How can you turn 6 into a negative 2?  You can subtract 8!  However, remember that what you do to one part of the inequality, you must do to each part of the inequality.

6 - 8 ≤ p - 8 ≤ 10 - 8

-2 ≤ p - 8 ≤ 2

Does that look like any of your answer choices?  Yes!  The answer that you found is just another way of writing that the absolute value of p - 8 is less than or equal to 2.