Since I can't see the figure I beleive you meant that B is the midpoint of AC. If this is true then the length from A to B is = the length from B to C. in other words. AB = BC and by segment addition postulate AB + BC = AC so (5x + 2 ) + (5x + 2) = 12x-2. Solve that algebra problem:
10x + 4= 12x-2 subtract 10x from both sides
4 = 2x - 2 add 2 to both sides
6 = 2x divide both sides by 2
3 = x you must now plug the x value back into AB = 5x+2= 5*3+2=17
since Ab = BC BC also = 17. This will make AC 34.
In the figure below, B is the midpoint of , AB = 5x + 2, and AC = 12x – 2.
What is the value of BC?
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