The incenter tells you two things
1. It is where the bisectors meet. This fact creates the next statement.
2. It is the same distance from the incenter to the sides of triangle. Three lines each drawn from the incenter perpendicularly to the sides will create 3 equal lines. These lines will each be equal. Put another way AI = BI = CI which are radii for the incircle.
Any two of AI, BI, and CI and make them equal to each other.
3x + 7 = 5x - 11 Now you can just use algebra to solve. Add 11 to both sides
3x + 7 + 11 = 5x
3x + 18 = 5x. Now subtract 3x from both sides.
18 = 5x - 3x
18 = 2x
x = 9
You should really check this. Do this by equating CI to either AI or BI. I leave it to you to figure out which one I choose.
Check
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This will be short so you can fill in the steps for yourself.
3x + 7 = 52 - 2x
5x = 45
x = 45/5
x = 9
