# How to write an absolute value inequality from words to expressions

Represents the solution set as a conjunction rather than a disjunction. Writes only the first inequality correctly but is unable to correctly solve it.

We just need to insure that out output is nonnegative. Why or why not? Got It The student provides complete and correct responses to all components of the task.

Does not represent the solution set as a disjunction. Examples of Student Work at this Level The student: Uses the wrong inequality symbol to represent part of the solution set. How did you solve the first absolute value inequality you wrote? Examples of Student Work at this Level The student correctly writes and solves the first inequality: The two statements above are needed to define absolute value in order to insure that the output of an absolute value function is NEVER less than zero.

Questions Eliciting Thinking Would the value satisfy the first inequality?

Try the following few calculations on your calculator: Examples of Student Work at this Level The student correctly writes and solves the absolute value inequality described in the first problem.

While this last statement looks more complicated than the beginning statement of 4 - 5x ,it is in a form that can be added, graphed, integrated calculus or differentiated calculus. You will investigate addition, integration, and differentiation in a later course.

Jo Steig The absolute value symbol is really shorthand for what we call a piecewise described function. When the inside expression includes variables and you do not know anything about the values of the variables, then writing the expression without absolute values takes a bit more care and our reliance on the definition above becomes more obvious.

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

The following example shows that process in detail. Can you reread the first sentence of the second problem?

Write 4 - 5x without using absolute value Solution: The end result will be a piecewise defined function that is similar to the original definition that was given above for absolute value.

The expression inside the absolute value is 4 - 5x. Can you describe in words the solution set of the first inequality? Instructional Implications Model using absolute value inequalities to represent constraints or limits on quantities such as the one described in the second problem.

A difference is described between two values. What is the constraint on this difference? Therefore, to get any work done we must first write it without absolute values.

Provide additional examples of absolute value inequalities and ask the student to solve them. Can you explain what the solution set contains?

The following three examples illustrate 1. Review, as needed, how to solve absolute value inequalities. If needed, clarify the difference between a conjunction and a disjunction. This is similar to receiving a computer disk on which the information has been condensed to save space.

How can you represent the absolute value of an unknown number? Write 5 - x without using absolute value Is unable to correctly write either absolute value inequality. What would the graph of this set of numbers look like? Our decompression program for the absolute value is the definition given above.

Model using simple absolute value inequalities to represent constraints or limits on quantities such as the one described in the second problem.

The reasoning here is similar to the last example. This is true because as long as x is larger than 4, x - 4 will be positive. Provide additional contexts and ask the student to write absolute value inequalities to model quantities or relationships described.

Write 2x - 3 without using absolute value In other words, all the points between –3 and 3, not one. DO NOT try to write this as one inequality. If you try to write this solution as "–2 > x > 2", you will probably be counted wrong: if you Find the absolute-value inequality statement that.

Introduction to Algebraic Expressions. What is a Variable? What Are Some Words We Use To Write Inequalities?

This tutorial shows you how to translate a word problem to an absolute value inequality.

Then see how to solve for the answer, write it in set builder notation, and graph it on a number line. This tutorial shows you how to translate a word problem to an absolute value inequality. Then see how to solve for the answer, write it in set builder notation, and graph it on a number line.

Learn all about it in this tutorial! If the expression inside the absolute value includes a variable, there is not much we can do with it as long as the absolute values are there. Therefore, to get any work done we must first write it without absolute values.

Absolute value inequalities word problem.

Now, they want us to write an absolute value inequality that models this relationship, and then find the range of widths that the table leg can be. So the way to think about this, let's let w be the width of the table leg.

So if we were to take the difference between w andwhat is this? How to write an expression in an equivalent form without absolute values? Ask Question. All you have to do is write down what the absolute value means. The definition we have is |x|:=\begin{cases}x&\text{ if }x\ge0\\-x&\text{ if }x.

How to write an absolute value inequality from words to expressions
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