Explain the differences between solving Absolute Value Equations and regular equations

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Explain the differences between solving Absolute Value Equations and regular equations.

How do I know when absolute value inequalities are "AND" or "OR" compound inequalities?

Oct 29th, 2015

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Part A

The absolute value of any number suppose "x" is written as |X| and it is always positive.

An absolute value equation is the equation is written as y=|x|.

So we can say that y =+x or -x,as on substituting negative or positive value of x the equation holds true.

Suppose,|X|=3 then on substituting x=-3 or 3 we get 3 as same on the right side.

But in a regular equation is is not like that,for the above example x=3,it satisfies only one value of x that is 3 and not -3.

Part B

"AND" or "OR" compound inequalities

A compound inequality contains at least two inequalities that are separated by either "and" or "or".

The graph of a compound inequality with an "and" represents the intersection of the graph of the inequalities. A number is a solution to the compound inequality if the number is a solution to both inequalities. It can either be written as x > -1 and x < 2 or as -1 < x < 2.

The graph of a compound inequality with an "or" represents the union of the graphs of the inequalities. A number is a solution to the compound inequality if the number is a solution to at least one of the inequalities. It is written as x < -1 or x > 2



Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 29th, 2015

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