why is the absolute value of 5x+3 > -2 all real numbers?

Question

We got his question in math today and my teacher didn't really explain how it is real numbers and I just want to make sure I understand.

Answer 1

You can also look at this problem graphically.

 

 

y = |5x + 3| is a 'V' graph that is above the x-axis except at x = -3/5 where it touches it.

 

 

y is never negative, so it is always greater than a negative number such as -2.

 

 

So, |5x + 3| > -2 for every x. 

Answer 2

l5x+3l>-2

5x+3>-2

5x>-5

x>-1

or, because it's absolute value...

-(5x+3)>-2

-5x-3>-2

-5x>1

x<(-1/5)   (you change the sign when dividing by a negative number)

the solution is x>-1 or x<(-1/5)

 

<-----l------l------l------l-----l------l----->

        -3     -2     -1       0     1       2      

                          ----------------------------------->

                                  x>-1

<------------------------

          x<(-1/5)

looking at the number line the two solutions (lines) overlap giving you all the real numbers