SOLUTION: 3/5X_<-54 -1/3X<-27 please and sooooo many thank yous!

Algebra ->  Inequalities -> SOLUTION: 3/5X_<-54 -1/3X<-27 please and sooooo many thank yous!      Log On


   

Question 115227: 3/5X_<-54



-1/3X<-27
please and sooooo many thank yous!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1

%283%2F5%29x%3C=-54 Start with the given inequality



%285%29%28%283%2F5%29x%29=%285%29%28-54%29 Multiply both sides by 5.


3x=-270 Multiply



x%3C=%28-270%29%2F%283%29 Divide both sides by 3 to isolate x



x%3C=-90 Divide

--------------------------------------------------------------
Answer:
So our answer is x%3C=-90



Now let's graph the solution set



Start with the given inequality:

x%3C=-90

Set up a number line:
number_line%28500%2C-100%2C-80%29

Now plot the point x=-90 on the number line


number_line%28500%2C-100%2C-80%2C+-90%29


Now pick any test point you want, I'm going to choose x=0, and test the inequality x%3C=-90


0%3C=-90 Plug in x=0


Since this inequality is not true, we simply shade the entire portion that does not contain the point x=0 using the point x=-90 as the boundary. This means we shade everything to the left of the point x=-90 like this:
Graph of x%3C=-90 with the shaded region in blue
note: at the point x=-90, there is an closed circle. This means the point x=-90 is included from the solution set.




#2



%28-1%2F3%29x%3C-27 Start with the given inequality



%283%29%28%28-1%2F3%29x%29=%283%29%28-27%29 Multiply both sides by 3


-1x=-81 Multiply



x%3E%28-81%29%2F%28-1%29 Divide both sides by -1 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)



x%3E81 Divide

--------------------------------------------------------------
Answer:
So our answer is x%3E81


Now let's graph the solution set




Start with the given inequality:

x%3E81

Set up a number line:
number_line%28500%2C71%2C91%29

Now plot the point x=81 on the number line


number_line%28500%2C71%2C91%2C+81%29


Now pick any test point you want, I'm going to choose x=0, and test the inequality x%3E81


0%3E81 Plug in x=0


Since this inequality is not true, we simply shade the entire portion that does not contain the point x=0 using the point x=81 as the boundary. This means we shade everything to the right of the point x=81 like this:
Graph of x%3E81 with the shaded region in blue
note: at the point x=81, there is an open circle. This means the point x=81 is excluded from the solution set.