How to write and solve an absolute value equation with one solution

One more important piece of information that you must remember is: Remove the absolute value bars by setting up a compound inequality. Also, we will always use a positive value for distance.

However, this is a time- consuming lesson, so I may assign the Exit Slip as homework if the Guided Practice ran long. Sciencing Video Vault 1.

Absolute Value in Algebra

The absolute value MUST be by itself on one side of the equation before splitting into two equations. My expectation is for my students to hand in the Slip before they leave. I ask, "What points on the number line are a distance of three units from zero?

You never know when one of those solutions is not going to be an actual solution to the equation. This new rule is: Therefore, if you end up with a scenario such as: 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: If you plot the above two equations on a graph, they will both be straight lines that intersect the origin.

This will happen on occasion when we solve this kind of equation with absolute values. Example 3 - Isolate the Absolute Value In this lesson, I hope that you have realized that you must isolate the absolute value expression before writing your two equations.

Example 3 Solve each of the following. This time we will need to divide in order to get the absolute value by itself on one side of the equation. One way to think of absolute value is that it takes a number and makes it positive.

Identifying weaknesses in my own teaching The purpose of this lesson is for my students to develop a conceptual understanding of what absolute value means, and apply it to solving Absolute Value Equations and Inequalities.

When we discuss the activity, table partners will share their responses from the activity, explaining why they chose what the answers that they did. That is exactly what this equation is saying however. The other partner either agrees or disagrees.

From this we can get the following values of absolute value. Is the number on the other side a negative number?Can an absolute value equation ever have and infinite amount of solutions?

What do you do when you have absolute values on both sides of the equations? How do you solve for m given #|\frac{m}{8}|=1#?

Solve One Equation for the Positive Value. x + y = 4x -3y.

Absolute Value Inequalities

4y = 3x. x = (4/3)y. This is solution for equation 1. This is the solution for equation 2. Because the original equation contained an absolute value, you're left with two relationships between x and y that are equally true.

"How to Write an Absolute-Value Equation That Has Given.

Solving Absolute Value Equations and Inequalities (Day 1 of 2)

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. Share your strategy for identifying and solving absolute value equations and inequalities on the discussion board. Make your own examples of absolute value equations and inequalities that have no solution, at least one for each case described in this section.

Solving equations with absolute value is a more advanced skill. For most absolute value equations, you will need to write two equations to solve.

Therefore, you will most likely end up with two answers to the equation. which will demonstrate how only one solution is the correct answer to the actual equation.

Solve the absolute value equation. Write the solution in set notation. |5m+2|=15

Example 1 - One Solution. 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 equations and absolute value inequalities.

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How to write and solve an absolute value equation with one solution
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