SAT absolute value problems are one of those sneaky topics that can pop up on the test and catch you off guard. They aren’t super common, so you may not even run into one when you take an SAT practice test, but it *is *a topic that’s sometimes tested on the SAT.

If you’ve mastered the more common SAT math topics (like linear equations and linear inequalities) and you’re ready to work through some of the less common topics, this is a great place to start. We’ll cover everything you need to know about absolute value for the SAT.

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## What is Absolute Value?

First things first. An absolute value looks like this:

Or this.

Or even this.

Get the idea? It’s anything with those bars on either side. The bars tell us to take the absolute value of whatever is inside.

But let’s back up. What *is *absolute value?

Absolute value tells us how far a number is from zero on the number line. It’s a *distance *measurement. And the key thing to remember is that **distance is always positive. ** You can’t be -5 miles from your school. You’re just 5 miles from school. This rings true for absolute value. Let’s walk through this using a number line.

How far is 3 from zero on the number line?

3 is 3 places from zero.

This takes us all the way back to when we first learned counting. Simple, right?

What about -3? How far is -3 from zero on the number line?

It’s still 3 places from zero.

When we take the absolute value of a number, we’re determining how far it is from zero on the number line.

## How Many Absolute Value Problems are on the SAT?

This is an important question to ask about *any * SAT math topic. Topic frequency can help you prioritize which topics to study during test prep.

SAT absolute value problems are quite rare. You’ll either have 0 or 1 absolute value problems on the SAT Math section. So, basically, a 50/50 shot of seeing this topic at all.

So, before you spend too much time on absolute value problems, make sure you’re very confident in your ability to solve linear equation questions, which are far more frequently tested.

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## How is Absolute Value Tested on the SAT?

Once you’ve answered the question “what is absolute value,” you’re ready to tackle how this concept is tested on the SAT.

Absolute value problems can be tested as:

- Equations containing an absolute value
- Linear inequalities containing an absolute value

Let’s look back at the first example we talked through. The absolute value of -3 and the absolute value of 3 are both 3.

|-3| = |3|

There are essentially two ways we can get to the “solution” of 3 here. We start with -3 or we start with 3. We can use this logic when we think about absolute value equations. Any time we have an absolute value in an equation, we have two possible solutions – two ways to get us to our end point.

**To solve absolute value problems on the SAT, we need to follow this process:**

- Turn the absolute value into two equations or inequalities (I’ll show you how to do this below)
- Solve both equations or inequalities
- Consider all solutions found when selecting your answer choice.

Let’s walk through an example of** **a** linear equation absolute value problem.**

## SAT Absolute Value SAT Problems

**Example 1:**

Following our steps, we’ll first turn each absolute value equation into two equations. Let’s start with the first equation.

We remove the absolute value bars, and the left side remains the same. On the right side, we flip the sign for the second equation. Doing this allows us to account for there being two possible solutions.

Solve.

We have two solutions for our first equation.

Now we need to follow the same process for the second equation.

Solve.

Going back to our question, we’re being asked which value of x satisfies both equations. In other words, which value of x is a solution for both equations.

Our answer would be x = 10 because this was a solution for both equations.

Now, let’s try a **linear inequality absolute value problem.**

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**Example 2:**

First, we turn this into two equations and we follow the same general rules as we did for **Example 2**. Drop the absolute value bars. Now, because we’re working with an inequality, we must flip *both *the inequality sign and the sign of the value on the right side.

Now solve both equations for x.

Putting it together, we get -4 < x < 9, so our answer is B.

**Example 3:**

There are two ways to tackle this question.

Option 1: Plug in your answer choices for x and test if you get 2.

Option 2: Solve the absolute value equation as we have done in **Examples 1 and 2 **above, by splitting it into two distinct equations.

Either option will work. One may take you longer than the other. It’s worth practicing to see which method you prefer (and which is faster). Let’s give Option 1 a try.

Plug in x = 5.

Does that work? Yes! So, we know 5 can work. But, don’t pull the trigger too quickly on answer A. We can eliminate B because it doesn’t include x= 5, but we could have multiple solutions for x, so we need to test answers C and D.

Plug in x = 1

Does that work? Yes again! Now we have our answer, C.

## Final Thoughts on Absolute Value for the SAT

SAT absolute value problems are rare. Expect to see either 0 or 1 questions that test absolute value. But, while rare, it’s a fairly straightforward topic that we recommend you take the time to review once you’ve mastered the more common SAT math topics.

Absolute value is all about computing the *distance *from zero on the number line. When solving SAT absolute value problems, it boils down to your ability to successfully split the given equation into two, accounting for the two solutions that are possible when dealing with absolute value.

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