Questions Eliciting Thinking Can you reread the first sentence of the second problem?
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Absolute Value Equations In the final two sections of this chapter we want to discuss solving equations and inequalities that contain absolute values. Before solving however, we should first have a brief discussion of just what absolute value is.
There are two ways to define absolute value. There is a geometric definition and a mathematical definition. We will look at both.
Also, we will always use a positive value for distance. Consider the following number line. From this we can get the following values of absolute value. One way to think of absolute value is that it takes a number and makes it positive. We do need to be careful however to not misuse either of these definitions.
There is also the fact however that the right number is negative and we will never get a negative value out of an absolute value! Well there are only two numbers that have a distance of 4 from the origin, namely 4 and So, this leads to the following general formula for equations involving absolute value.
Example 1 Solve each of the following. Example 2 Solve each of the following. This is saying that the quantity in the absolute value bars has a distance of zero from the origin.
There is only one number that has the property and that is zero itself. That is exactly what this equation is saying however. Likewise, there is no reason to think that we can only have one absolute value in the problem.
So, we need to take a look at a couple of these kinds of equations. Example 3 Solve each of the following. It requires the right side of the equation to be a positive number.
There is a problem with the second one however. This will happen on occasion when we solve this kind of equation with absolute values. So, all together there is a single solution to this equation: We only exclude a potential solution if it makes the portion without absolute value bars negative.Graph a piecewise Interpret an absolute value graph (Lesson 4 Write an absolute value equation given real-world constraints.
Interpret the solutions to an absolute value equation. (Lesson ) Write a system of three equations to represent a real-world scenario. (Lesson ) Solve a system of three equations. (Lesson ). A summary of Solving Equations Containing Absolute Value in 's Absolute Value.
Learn exactly what happened in this chapter, scene, or section of Absolute Value and what it means. Perfect for acing essays, tests, and quizzes, as well as for writing lesson plans. Solve and Graph Absolute Value Equations leslutinsduphoenix.com7B leslutinsduphoenix.com3 Digital copies of the worksheets, as well as hyperlinks to the videos listed on t he back are Write a two pieced piecewise-defined function, 𝑓𝑓, that accurately represents the graph of f shown above.
Worksheet: Piecewise Functions.
Evaluate the function for the given value of x. Match the piecewise function with its graph. Graph the function. Children between 12 years and 18 years, inclusive: $ Adults: $ a) Write a piecewise function that gives the admission price for a . While absolute-value graphs tend to look like the one above, with an "elbow" in the middle, this is not always the case.
However, if you see a graph with an elbow like this, you should expect that the equation is probably an absolute value. 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 .