# How to write an absolute value inequality from a compound inequality

So the first problem I have is negative 5 is less than or equal to x minus 4, which is also less than or equal to We just have to satisfy one of these two.

We know that negative 12 needs to be less than 2 minus 5x. And actually, you can do these simultaneously, but it becomes kind of confusing. This process can be a little confusing at first, so be patient while learning how to do these problems. Use the sign of each side of your inequality to decide which of these cases holds.

You get x is greater than or equal to 2. So our two conditions, x has to be greater than or equal to negative 1 and less than or equal to So first we can separate this into two normal inequalities.

So we could rewrite this compound inequality as negative 5 has to be less than or equal to x minus 4, and x minus 4 needs to be less than or equal to Isolate the absolute value expression on the left side of the inequality.

So that is our number line. If the number on the other side of the inequality sign is positive, proceed to step 3. The width has to be less than or equal to And since we divided by a negative number, we swap the inequality.

So the width of our leg has to be greater than So x can be greater than or equal to 2. The left-hand side, negative 5 plus 4, is negative 1. Let me get a good problem here. So we have our two constraints.

And I really want you to understand this. If your problem has a greater than sign your problem now says that an absolute value is greater than a numberthen set up an "or" compound inequality that looks like this: Here are the steps to follow when solving absolute value inequalities: So this is the first part.

The right-hand side becomes 7 minus 2, becomes 5. Then we would have a negative 1 right there, maybe a negative 2. We have written an absolute value inequality that models this relationship.

And if we wanted to write it in interval notation, it would be x is between negative 1 and 17, and it can also equal negative 1, so we put a bracket, and it can also equal So the left, this part right here, simplifies to x needs to be greater than or equal to negative 1 or negative 1 is less than or equal to x.

And remember, when you multiply or divide by a negative number, the inequality swaps around.Solving Absolute Value Equations and Inequalities 51 An absolute value inequality such as |x º 2|.

The absolute value inequality I31 - sI ≤ 8 represents this situation. If the compound inequality -x ≤ 31 - s and x ≥ 31 - s also represents this situation, what is the value of x in the compound inequality? Watch video · Compound inequalities: AND. Practice: Compound inequalities.

A compound inequality with no solution.

Double inequalities. So we could write this again as a compound inequality if we want.

We can say that the solution set, that x has to be less than or equal to 17 and greater than or equal to negative 1. It has to satisfy. How do you write the compound inequality as an absolute value inequality: ≤ h ≤ ?

Algebra Linear Inequalities and Absolute Value Absolute Value Inequalities. 1 Answer Adrian D.

Jul 11, Are all absolute value inequalities going to turn into compound inequalities? Free absolute value inequality calculator - solve absolute value inequalities with all the steps. Type in any inequality to get the solution, steps and graph Absolute. Pre Algebra. Absolute Value Inequalities Calculator Solve absolute value inequalities, step-by-step.

Equations. Basic (Linear) Solve For. Apr 15,  · 16 Compound inequality with absolute value Khan Academy. Solving Compound and Absolute Value Inequalities - Duration: How To Solve Absolute Value Inequalities.

How to write an absolute value inequality from a compound inequality
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