# How do you write an absolute value inequality

The absolute value is always positive, so you can think of it as the distance from 0. I like to then make the expression on the right hand side without the variables both positive and negative and split the equation that way. In this case our answer is all real numbers, since an absolute value is always positive.

Here are more problems: Try the answers in the original equation to make sure they work! Note that we still have to simplify first to separate the absolute value from the rest of the numbers. Check the answers; the work!

Note that we get some complex roots since we had to take the square root of a negative number. We need to treat the absolute value like a variable, and get it out from the denominator by cross multiplying. Then we can continue to solve, and divide up the equations to get the two answers.

Check the answers — they work! In this case, we have to separate in four cases, just to be sure we cover all the possibilities. Solving Absolute Value Inequalities When dealing with absolute values and inequalities just like with absolute value equationswe have to separate the equation into two different ones, if there are any variables inside the absolute value bars.

## Compound inequalities

We first have to get the absolute value all by itself on the left. Now we have to separate the equations. We get the first equation by just taking away the absolute value sign away on the left. The easiest way to get the second equation is to take the absolute value sign away on the left, and do two things on the right: Here are some examples: Even with the absolute value, we can set each factor to 0, so we get —4 and 1 as critical values.

Then we check each interval with random points to see if the factored form of the quadratic is positive or negative, making sure we include the absolute value. Then we need to get everything to the left side to have 0 on the right first.

Simplify with a common denominator. We see the solution is: Graphs of Absolute Value Functions Note that you can put absolute values in your Graphing Calculator and even graph them!

Absolute Value functions typically look like a V upside down if the absolute value is negativewhere the point at the V is called the vertex.Rational Absolute Value Problem.

Notes. Let’s do a simple one first, where we can handle the absolute value just like a factor, but when we do the checking, we’ll take into account that it is an absolute value.

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Students are asked to write absolute value inequalities to represent the relationship among values described in word problems.

Whereas the inequality $$\left | x \right |>2$$ Represents the distance between x and 0 that is greater than 2. You can write an absolute value inequality as a compound inequality. $$\left | x \right |0$$ $$=-cc,\: where\: c>0$$ $$=ax+bc$$ You can replace > .

How to Solve Absolute Value Inequalities? (13 Surefire Examples!)