Ineed some really fast which value of x is in the solution set of 2|x – 3| < 4?
a.
x = 8
b.
x = 0
c.
x = 4
d.
x = –1

Well I don't know.  Let me check them and find out.  In fact, let's you and me both together check them and find out.  When we're done, you'll see that you could have done that on your own, and you'll know how to do it on your own next time you run into a similar problem.

How can you take a value of 'x' and see whether it's a solution to an equation ?
Just write the value in place of 'x' in the equation, and see whether that makes
the equation a true statement.

The equation is   2 |x-3|  <  4 .
We'll test each choice against that equation.

Remember what  |a number| means ?
It means the raw size of that number, without worrying about
whether it's a positive or negative number.
In other words, it just means take the number inside the bars
and throw away the sign.  Just call it a positive number.

First choice:  x=8
Try it out:              2 |x-3|  <  4
                             2 |8-3|  <  4
                             2 | 5 |  < 4
                               10    <  4       <--- That is not a true statement.
                                                           So x=8 is not a solution to the equation. 

Second choice:  x = 0
Try it out:                      2 |x-3|  <  4
                                     2 |0-3|  < 4
                                     2 | -3 |  < 4
Remember  |-3|  is just 3.   
                                     2 ( 3 )  <  4
                                         6     <  4     <--- That is not a true statement.
                                                             So  x=0  is not a solution to the equation. 

Third choice:  x = 4
Try it out:                  2 |x-3|  <  4
                                 2 |4-3|  <  4
                                 2 | 1 |   <  4
                                     2      <  4    <--- That is a true statement.
                                                              So  x=4  is a solution to the equation. 

                                                    It may not be the only one.
                                                    We still need to check out the remaining choice.

Fourth choice:  x = -1
Try it out:                      2 |x-3|  <  4
                                     2 |-1-3| < 4
                                     2 | -4 |  < 4
Remember that  | -4 | is just 4 .
                                     2 (4)    < 4
                                       8        < 4    <--- That is not a true statement.
                                                           So  x= -1 is not a solution to the equation. 

There are a huge number of solutions to the equation.
But there are also a huge quantity of numbers that are not solutions.
Out of the choices that were given, only one of them worked.

Choice 'C':  x = 4 .

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