SOLUTION: solve and graph on a number line -x over 4 is greater than 3

Algebra ->  Rational-functions -> SOLUTION: solve and graph on a number line -x over 4 is greater than 3      Log On


   

Question 118333: solve and graph on a number line -x over 4 is greater than 3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-x%2F4%3E3 Start with the given inequality



cross%284%29%28-x%2Fcross%284%29%29=%284%29%283%29 Multiply both sides by 4.


-x=12 Multiply



x%3C%2812%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%3C-12 Divide

--------------------------------------------------------------
Answer:
So our answer is x%3C-12



Now let's graph the solution set


Start with the given inequality:

x%3C-12

Set up a number line:
number_line%28500%2C-22%2C-2%29

Now plot the point x=-12 on the number line


number_line%28500%2C-22%2C-2%2C+-12%29


Now pick any test point you want, I'm going to choose x=0, and test the inequality x%3C-12


0%3C-12 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=-12 as the boundary. This means we shade everything to the left of the point x=-12 like this:
Graph of x%3C-12 with the shaded region in blue

note: at the point x=-12, there is an open circle. This means the point x=-12 is excluded from the solution set.