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

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) (Show Source): You can put this solution on YOUR website!
Start with the given inequality

Subtract 7x from both sides

Combine like terms on the left side

Divide both sides by -3 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)

Reduce

--------------------------------------------------------------
Answer:
So our answer is (which is approximately in decimal form)

Now let's graph the solution set

Start with the given inequality:

Set up a number line:

Now plot the point on the number line

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

Plug in

Since this inequality is not true, we simply shade the entire portion that does not contain the point x=0 using the point as the boundary. This means we shade everything to the left of the point like this:
Graph of with the shaded region in blue

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

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