how do i solve the following inequality 20 + 6z > 12z - 13

Question

help solve the following inequality

 

Answer 1

Hello there, CJ

 

You must remember that you solve inequalities just like you solve equation, the only difference is that if you multiply or divide by a negative, you must change the sign of the inequality ( the direction where the arrow is pointing). Just like with equations, you can solve inequalities in a number of ways, but I suggest that you avoid dividing or multiplying by a negative because you might forget to switch the sign.  I see that mistake over, and over again when I am grading papers.  Ok, enough about me.. Let's get started

 

20+ 6z > 12z-13

+13               +13

  33+ 6z > 12z

         -6z    -6z

     33> 6z             Divide by 6 on both sides

      5.5>z  or z< 5.5

If we were to graph this, we would need an open circle on the 5.5 and shade the line to the left all the way... dont stop at zero... all the way.

 

Now, if you are confused about 5.5>z being the same as z< 5.5, let me give you an example.  3<5 is the same as 5> 3.  Let's say you have an older brother.  Saying that your brother is older than you, is the same as saying that you are younger than your brother.  Using inequalities, and using the variable u for you and the variable b, for your brother, this can be written as

 

u< b      You are younger than your brother.

b>u       Your brother is older than you.

 

Well, I threw that in because many of my students do not understand this concept.  Thus, they graph the inequality in the wrong direction.

 

Ok, CJ... I hope this helps out.. Please rate my answer:)

 

D. Y. T.