SOLUTION: Solve each inequality and graph the solution, HELP, please. -3a+10<-11

Algebra ->  Inequalities -> SOLUTION: Solve each inequality and graph the solution, HELP, please. -3a+10<-11      Log On


   

Question 96854: Solve each inequality and graph the solution, HELP, please.
-3a+10<-11
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-3a%2B10%3C-11 Start with the given inequality


-3a%3C-11-10Subtract 10 from both sides


-3a%3C-21 Combine like terms on the right side


a%3E%28-21%29%2F%28-3%29 Divide both sides by -3 to isolate a (note: dividing by both sides by a negative number flips the inequality sign)



a%3E7 Divide

--------------------------------------------------------------
Answer:
So our answer is a%3E7



Now let's graph the solution




Start with the given inequality:

a%3E7

Set up a number line:
number_line%28500%2C-3%2C17%29 note: just replace the x with the variable you are working with


Now plot the point a=7 on the number line


number_line%28500%2C-3%2C17%2C+7%29


Now pick any test point you want, I'm going to choose a=0, and test the inequality a%3E7


0%3E7 Plug in a=0


Since this inequality is not true, we simply shade the entire portion that does not contain the point a=0 using the point a=7 as the boundary. This means we shade everything to the right of the point a=7 like this:
Graph of a%3E7 with the shaded region in blue
note: at the point a=7, there is an open circle. This means the point a=7 is excluded from the solution set.