SOLUTION: solve the inequality. then graph the solution. 3x+3 < x+5

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Question 118125: solve the inequality. then graph the solution.
3x+3 < x+5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%2B3%3Cx%2B5 Start with the given inequality



3x%3Cx%2B5-3Subtract 3 from both sides


3x-x%3C5-3 Subtract x from both sides


2x%3C5-3 Combine like terms on the left side


2x%3C2 Combine like terms on the right side


x%3C%282%29%2F%282%29 Divide both sides by 2 to isolate x



x%3C1 Divide

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Answer:
So our answer is x%3C1



Now let's graph the solution set


Start with the given inequality:

x%3C1

Set up a number line:
number_line%28500%2C-9%2C11%29

Now plot the point x=1 on the number line


number_line%28500%2C-9%2C11%2C+1%29


Now pick any test point you want, I'm going to choose x=0, and test the inequality x%3C1


0%3C1 Plug in x=0


Since this inequality is true, we simply shade the entire portion in which contains the point x=0 using the point x=1 as the boundary.This means we shade everything to the left of the point x=1 like this:
Graph of x%3C1 with the shaded region in blue

note: at the point x=1, there is an open circle. This means the point x=1 is excluded from the solution set.