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

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

Start with the given inequality

Distribute

Add 12 to both sides

Subtract 7x from both sides

Combine like terms on the left side

Combine like terms on the right side

Divide both sides by -4 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)

Reduce

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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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