# How to write an absolute value equation with given solutions

A difference is described between two values. For example, represent the difference between x and 12 as x — 12 or 12 — x. Equation 2 is the correct one.

Instructional Implications Model using absolute value to represent differences between two numbers. Finds only one of the solutions of the first equation. Emphasize that each expression simply means the difference between x and If needed, clarify the difference between an absolute value equation and the statement of its solutions.

Writing an Equation with a Known Solution If you have values for x and y for the above example, you can determine which of the two possible relationships between x and y is true, and this tells you whether the expression in the absolute value brackets is positive or negative.

This is the solution for equation 2. What is the difference?

Questions Eliciting Thinking Can you reread the first sentence of the second problem? Guide the student to write an equation to represent the relationship described in the second problem.

Plug in known values to determine which solution is correct, then rewrite the equation without absolute value brackets. What are these two values? Examples of Student Work at this Level The student correctly writes and solves the first equation: Ask the student to solve the equation and provide feedback.

Should you use absolute value symbols to show the solutions? Got It The student provides complete and correct responses to all components of the task. Examples of Student Work at this Level The student: Sciencing Video Vault 1. If you already know the solution, you can tell immediately whether the number inside the absolute value brackets is positive or negative, and you can drop the absolute value brackets.

If you plot the above two equations on a graph, they will both be straight lines that intersect the origin. Do you know whether or not the temperature on the first day of the month is greater or less than 74 degrees? Provide additional opportunities for the student to write and solve absolute value equations.

Ask the student to consider these two solutions in the context of the problem to see if each fits the condition given in the problem i.

Writes the solutions of the first equation using absolute value symbols. Do you think you found all of the solutions of the first equation? Set Up Two Equations Set up two separate and unrelated equations for x in terms of y, being careful not to treat them as two equations in two variables: Plug these values into both equations.

When you take the absolute value of a number, the result is always positive, even if the number itself is negative. Instructional Implications Provide feedback to the student concerning any errors made. 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 This is solution for equation 1.

To solve this, you have to set up two equalities and solve each separately. This means that any equation that has an absolute value in it has two possible solutions.

What are the solutions of the first equation? Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem? Then explain why the equation the student originally wrote does not model the relationship described in the problem.

Questions Eliciting Thinking How many solutions can an absolute value equation have? You can now drop the absolute value brackets from the original equation and write instead: For a random number x, both the following equations are true:Remember that an absolute value represents a distance from zero, so if we are given two solutions and asked to write an absolute value equation, we'll somehow need to figure out what is the starting place (like zero) and how far should we be traveling in each direction to arrive at those solutions.

You can put this solution on YOUR website! 9 and 21 differ by Sinxe half of 12 is 6, we want the absolute value part to result in the values 6 and -6 in the equation. Solve Equations with Absolute Value. Using the factor theorem, we can write two simpler equations x + 2 = 0 or x - 3 = 0 The solutions to the given equation are x = -2, x = 1 and x = 3.

Matched Exercise 4: Solve the equation |x 2 - 16 | = x -. Solve an absolute value equation using the following steps: Get the absolve value expression by itself.

Set up two equations and solve them separately. Solved: Write and absolute value equation that has the given solutions of x=3 and x=9 - Slader/5(1). How to Write an Absolute-Value Equation That Has Given Solutions By Chris Deziel; Updated April 25, You can denote absolute value by a pair of vertical lines bracketing the number in question.

How to write an absolute value equation with given solutions
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