If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions. The solution for each of these is then all real numbers.

The type of inequality sign in the problem will tell us how to set up the compound inequality.

Example 3 Solve each of the following. If the number on the other side of the inequality sign is positive, proceed to step 3. Is unable to correctly write either absolute value inequality.

In a double inequality we require that both of the inequalities be satisfied simultaneously. Examples of Student Work at this Level The student correctly writes and solves the first inequality: If needed, clarify the difference between a conjunction and a disjunction.

Set up a compound inequality The inequality sign in our problem is a less than sign, so we will set up a 3-part inequality: Remove the absolute value bars by setting up a compound inequality.

Instructional Implications Model using absolute value inequalities to represent constraints or limits on quantities such as the one described in the second problem. Example 1 Solve each of the following. Absolute Value Inequalities In the previous section we solved equations that contained absolute values.

Is the number on the other side negative? Example 2 Solve each of the following.

Use the sign of each side of your inequality to decide which of these cases holds. However, the student is unable to correctly write an absolute value inequality to represent the described constraint. Got It The student provides complete and correct responses to all components of the task.

Instructional Implications Provide feedback to the student concerning any errors made in solving the first inequality or representing its solution set.

Due to the nature of the mathematics on this site it is best views in landscape mode. Provide additional contexts and ask the student to write absolute value inequalities to model quantities or relationships described. Here are the steps to follow when solving absolute value inequalities: A difference is described between two values.

Therefore, in this case there is no solution since it is impossible for an absolute value to be strictly less than zero i. What is the constraint on this difference?

Can you reread the first sentence of the second problem? If your absolute value is less than a number, then set up a three-part compound inequality that looks like this:Oct 26, · How to write an absolute value inequality from a graph. Writing an Absolute Value Inequality from a Graph MsDenham Solving an absolute value inequality with a quadratic - Duration.

The other case for absolute value inequalities is the "greater than" case. Let's first return to the number line, and consider the inequality | x | > The solution will be all points that are more than two units away from zero.

Students are asked to write absolute value inequalities to represent the relationship among values described in word problems. the student is unable to correctly write an absolute value inequality to represent the described constraint.

Can you describe in words the solution set of the first inequality? For each problem, write an absolute value equation and two inequalities that can be solved using the given graph.

Then, solve, write the solution set in set-builder notation, and graph the solution. Oct 21, · In this video, I introduce and explain a pattern that can be used to write an absolute value inequality from a number line graph. I do three different examples, one being a simple word problem.

These absolute value word problems in this lesson will explore real life situations that can be modeled by either an absolute value equation or an absolute value inequality.

You may need to review the lesson about how to solve absolute value .

DownloadHow to write an absolute value inequality from words to pictures

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