Compound Absolute Values Equalities and Inequalities More than one absolute value in the equation.

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Compound Absolute Values Equalities and Inequalities More than one absolute value in the equation

Find a number that works. Well, how can you find all of the solutions in a more methodical way?

In your approach, think about the values of this particular mathematical statement in the 3 different areas on this number line

What happens in the expression as x goes from area 1, to area II, to area III? IIIIII

This is a “domain limiting problem”. How does limiting the values that I am considering for x help me evaluate the equation? Look at these 3 equations to see if you can figure out how we will limit the domain.

Lets try a problem

We need a process 1.Draw a number line to create areas of consideration (i.e. Limit the domain!!) 2.Determine the value of each absolute value in each area (that is, is each absolute value positive or negative) and remove absolute values based on that. 3.Solve the equation. 4. See where the domain overlaps with the answer for each area.

Why? If we pick a domain of possible answers, the solution of the equation gives the answers IN THE DOMAIN that actually work. So, the overlap (the intersection) of the two sets will be the answer for that particular limitation.

What does this mean? Each case will be an “and” within the case (domain w/answer) Take the 3 answers (case 1, case 2, case 3) and combine as an “or”.