SOLUTION: Solve and graph the solution set. 3x is less than or equal to 7x + 20

Question 117483: Solve and graph the solution set. 3x is less than or equal to 7x + 20
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 -4 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)

Divide

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Answer:
So our answer is

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 true, we simply shade the entire portion in which contains the point x=0 using the point as the boundary.This means we shade everything to the right of the point like this:
Graph of with the shaded region in blue
note: at the point , there is an closed circle. This means the point is included from the solution set.

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