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

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 what would that look like on a number line?

You have to meet both of these constraints. Maybe this is 0. If needed, clarify the difference between a conjunction and a disjunction. Maybe this is 0, this is 1, this is 2, 3, maybe that is negative 1. And since we divided by a negative number, we swap the inequality. Isolate the absolute value expression on the left side of the inequality.

Is the number on the other side negative? And then we could solve each of these separately, and then we have to remember this "and" there to think about the solution set because it has to be things that satisfy this equation and this equation.

Review, as needed, how to solve absolute value inequalities. How can you represent the absolute value of an unknown number? Questions Eliciting Thinking Would the value satisfy the first inequality?

You add 1 to both sides. Writes only the first inequality correctly but is unable to correctly solve it. Examples of Student Work at this Level The student correctly writes and solves the absolute value inequality described in the first problem.

The left-hand side just becomes 4x is greater than or equal to 7 plus 1 is 8. I want to do a problem that has just the less than and a less than or equal to. Can you describe in words the solution set of the first inequality? And this is interesting. This tells us, how much of an error did we make?

Provide additional contexts and ask the student to write absolute value inequalities to model quantities or relationships described. We know that negative 12 needs to be less than 2 minus 5x.

So x is greater than or equal to negative 1, so we would start at negative 1. 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.

In order for the leg to fit, it needs to be millimeters wide, allowing for a margin of error of 2. So the width of our leg has to be greater than Represents the solution set as a conjunction rather than a disjunction.

Anyway, hopefully you, found that fun. What do we get?

We just have to satisfy one of these two. Examples of Student Work at this Level The student: Or it has to be greater than or equal to, or we could say The type of inequality sign in the problem will tell us how to set up the compound inequality.

It goes from less than or equal to, to greater than or equal to.

So if you subtract 2 from both sides of the equation, the left-hand side becomes negative 5x. Set up a compound inequality The inequality sign in our problem is a greater than or equal to sign, so we will set up a compound inequality with the word "or": So if you divide both sides by negative 5, you get a negative 14 over negative 5, and you have an x on the right-hand side, if you divide that by negative 5, and this swaps from a less than sign to a greater than sign.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. Find the mid-point between the extremes of the inequality and form the equality around that to reduce it to single inequality. the mid-point is so. 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? Solving Absolute Value Inequalities Involving ‘Greater Than’ (subtract \$\,7\,\$ from all three parts of the compound inequality) Solve the given absolute value sentence.

Write the result in the most conventional way. For more advanced students, a. A special type of compound inequality involves the absolute value sign. The absolute value sign specifies two functions such that f(x)=A implies f(-x) = (-A)(-1).

For the equal sign this is the same as f(x)=f(-x)=A. What Are Some Words We Use To Write Inequalities?

Knowing the definition for a compound inequality is one thing, but being able to identify one in a word problem or phrase can be an entirely different challenge. Arm yourself by learning some of the common phrases used to describe a compound inequality and an absolute value .

How to write an absolute value inequality as a compound inequality
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