SOLUTION: Solve and graph the solution set of 4x > 7x + 20. If a unique solution does - not exist, state whether the system is dependent or inconsis

Algebra ->  Inequalities -> SOLUTION: Solve and graph the solution set of 4x > 7x + 20. If a unique solution does - not exist, state whether the system is dependent or inconsis      Log On


   

Question 128595: Solve and graph the solution set of 4x > 7x + 20. If a unique solution does
-
not exist, state whether the system is dependent or inconsistent.
I can't fiqure this one out
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4x%3E7x%2B20 Start with the given inequality



4x-7x%3E20 Subtract 7x from both sides


-3x%3E20 Combine like terms on the left side


x%3C%2820%29%2F%28-3%29 Divide both sides by -3 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)



x%3C-20%2F3 Reduce

--------------------------------------------------------------
Answer:
So our answer is x%3C-20%2F3 (which is approximately x%3C-6.667 in decimal form)




Now let's graph the solution set


Start with the given inequality:

x%3C-6.667

Set up a number line:
number_line%28500%2C-16.667%2C3.333%29

Now plot the point x=-6.667 on the number line


number_line%28500%2C-16.667%2C3.333%2C+-6.667%29


Now pick any test point you want, I'm going to choose x=0, and test the inequality x%3C-6.667


0%3C-6.667 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=-6.667 as the boundary. This means we shade everything to the left of the point x=-6.667 like this:
Graph of x%3C-6.667 with the shaded region in blue

note: at the point x=-6.667, there is an open circle. This means the point x=-6.667 is excluded from the solution set.