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

The following example shows that process in detail. Does not represent the solution set as a disjunction. Therefore, to get any work done we must first write it without absolute values.

This is true because as long as x is larger than 4, x - 4 will be positive. We just need to insure that out output is nonnegative. What is the constraint on this difference?

The student correctly writes the second inequality as or. Represents the solution set as a conjunction rather than a disjunction.

Instructional Implications Provide feedback to the student concerning any errors made in solving the first inequality or representing its solution set. Can you reread the first sentence of the second problem? What are these two values? Try the following few calculations on your calculator: 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.

Examples of Student Work at this Level The student: Can you explain what the solution set contains? If needed, clarify the difference between a conjunction and a disjunction. Write 2x - 3 without using absolute value 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 correctly writes and solves the first inequality: However, the student is unable to correctly write an absolute value inequality to represent the described constraint.

Writes only the first inequality correctly but is unable to correctly solve it. How did you solve the first absolute value inequality you wrote?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. 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? 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.

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.

When solving an absolute value inequality it's necessary to first isolate the absolute value expression on one side of the inequality before solving the inequality.

Example Solve the absolute value inequality. 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.

How to write an absolute value inequality from words to expressions
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