# Writing absolute value inequalities from word problems

So, we must use the greater than or equal to symbol. Can you explain what the solution set contains? Provide additional examples of absolute value inequalities and ask the student to solve them.

Do you think you found all of the solutions of the first equation? Evaluate the expression x — 12 for a sample of values some of which are less than 12 and some of which are greater than 12 to demonstrate how the expression represents the difference between a particular value and Examples of Student Work at this Level The student: A difference is described between two values.

At least is a key word that notes that this problem must be written as an inequality. Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem?

Model using simple absolute value inequalities to represent constraints or limits on quantities such as the one described in the second problem. Also look for key words such as "solve for" and "identify.

Once the inequality is written, you can solve the inequality using the skills you learned in our past lessons. Word Problem Solving Strategies Read through the entire problem. Solve We have an equation; now to solve it for the unknown.

Examples of Student Work at this Level The student correctly writes and solves the first equation: However, the student is unable to correctly write an absolute value inequality to represent the described constraint.

Well, word problems, but we meant no problem with—actually, nevermind. Instructional Implications Provide feedback to the student concerning any errors made in solving the first inequality or representing its solution set.

If we map out our equation first, using our language of choice, it will help us understand how to go about solving for the unknowns. Click here to move onto the word problem practice problems.

I know it always helps too, if you have key words that help you to write the equation or inequality. Ask the student to solve the equation and provide feedback. You could also substitute any number less than Examples of Student Work at this Level The student correctly writes and solves the first inequality: Assigning labels will help us transition from words to the equation that will ultimately lead to the answer.

Uses the wrong inequality symbol to represent part of the solution set. Got It The student provides complete and correct responses to all components of the task. Oh, you want to know what they are? This is one of the reasons why we read the problem so much in Step 1 and identify the unknowns in Step 2. How many miles can Katie travel without exceeding her budget?

Instructional Implications Model using absolute value to represent differences between two numbers. BACK The art of determining how and when math can and should be applied in the real world is all about translating. For example, represent the difference between x and 12 as x — 12 or 12 — x. Instructional Implications Provide feedback to the student concerning any errors made. All of this sounds simple enough when just talking about it, but go ahead and click on the Examples button up top to see the magic in action.

The student does not understand how to write and solve absolute value inequalities. Think about others ways you might use inequalities in real world problems. Provide additional contexts and ask the student to write absolute value inequalities to model quantities or relationships described.

Represents the solution set as a conjunction rather than a disjunction. Instructional Implications Model using absolute value inequalities to represent constraints or limits on quantities such as the one described in the second problem.

Examples of Student Work at this Level The student: How can you represent the absolute value of an unknown number? The number of weeks that Keith can withdraw money from his account is 12 weeks or less.

They get so excited about solving for a variable that they forget that they still need to check if that solution actually answers the question posed in the problem.I know that solving word problems in Algebra is probably not your favorite, but there's no point in learning the skill if you don't apply it.

I promise to make this as easy as possible. Pay close attention to the key words given below, as this will help you to write the inequality. However, the student is unable to correctly write an absolute value equation to represent the described difference.

Questions Eliciting Thinking Can you reread the first sentence of the second problem? Ask the student to identify and write as many equivalent forms of the second inequality as he or she can. Then have the student solve each form to show that they are equivalent. Consider implementing MFAS task Solving Absolute Value Inequalities (A-CED). A helpful way to solve any word problem is to first write an "equation" using words. That’s right, no numbers. This is a way to map out what we'll later replace with variables and numbers.

Absolute value word problems 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.

Page 1 of 2 50 Chapter 1 Equations and Inequalities Solving Absolute Value Equations and Inequalities SOLVING EQUATIONS AND INEQUALITIES The of a number x, written|x|, is the distance the number is from 0 on a number line. Notice that the absolute value of a .

Writing absolute value inequalities from word problems
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