can anyone help and give an example

Question

Describe how you know if an inequality is an “and” or an “or” problem. (use -3 < x+5 < 8). Also, how do you know if an absolute value question is an “and” or an “or” problem? Lastly, will you always have two solutions to an absolute value problem?

Answer 1

My question is what is an absolute value?  

 

The absolute value of a number is the distance (always positive) from the number to zero.  So any given number has 1 absolute value.  Now if you are asking something like 'solve for x where the absolute value of x + 4 = 8' then that kind of equation will almost always have '2 answers'.  One where x + 4 = 8 and one where x + 4 = -8.  Therefore x={-12,4}.  But why 'almost always'?  What if the question is 'solve for x where the absolute value of x + 4 = 0'?  Positive and negative zero are the same.  Therefore only one answer.

 

Now inequalities depend on the question.  The problem you gave asks for all values of x that make -3 < x+5 < 8 true.  When you do the subtract 5 (or add -5) from all the term the result is -8 < x < 3.  This is an and because x must be both greater than -8 and less than 3.  An example of an or result could be something like 'the absolute value of x + 5 is greater than 8.  Check out the above discussion of absolute value.  Draw the number line and play.  

Answer 2

Kendrick

            if you describe -3<x+5<8 in words it is x plus five is greater than negative three AND less than five does that give you a hint?

 

            Regarding the abs function there can be multiple solutions to Abs(x)=g(x) depending on the properties of g(x). If g(x)<0 there are no solutions.

 

           Hope this helps

Jim