SOLUTION: solve and graph the solution set. 3(x-4)>7x-9

Algebra ->  Graphs -> SOLUTION: solve and graph the solution set. 3(x-4)>7x-9      Log On


   

Question 110602: solve and graph the solution set.
3(x-4)>7x-9
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3%28x-4%29%3E7x-9 Start with the given inequality



3x-12%3E7x-9 Distribute


3x%3E7x-9%2B12Add 12 to both sides


3x-7x%3E-9%2B12 Subtract 7x from both sides


-4x%3E-9%2B12 Combine like terms on the left side


-4x%3E3 Combine like terms on the right side


x%3C%283%29%2F%28-4%29 Divide both sides by -4 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)



x%3C-3%2F4 Reduce

--------------------------------------------------------------
Answer:
So our answer is x%3C-3%2F4 (which is approximately x%3C-0.75 in decimal form)


Now let's graph the solution set


Start with the given inequality:

x%3C-3%2F4

Set up a number line:
number_line%28500%2C-13%2C7%29

Now plot the point x=-3%2F4 on the number line


number_line%28500%2C-13%2C7%2C+-3%2F4%29


Now pick any test point you want, I'm going to choose x=0, and test the inequality x%3C-3%2F4


0%3C-3%2F4 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=-3%2F4 as the boundary. This means we shade everything to the left of the point x=-3%2F4 like this:
Graph of x%3C-3%2F4 with the shaded region in blue

note: at the point x=-3%2F4, there is an open circle. This means the point x=-3%2F4 is excluded from the solution set.