Let A be between B and C. Use the segment addition postulate to solve for w.
BA = 7w − 12
AC = 6w − 14
jasmine
BA + AC = BC
7w-12 + 6w-14 = BC
13w-26 = BC
Now you need to know what BC is to find w. I suspect that BC is a multiple of 13, no?
According to the segment addition postulate, the sum of the lengths of two segments equals the length of the entire segment. In this case, segment BA and segment AC together make up segment BC.
So, using the segment addition postulate, we have:
BA + AC = BC
Substituting the given values:
(7w - 12) + (6w - 14) = BC
Simplifying the equation:
13w - 26 = BC
Therefore, BC is equal to 13w - 26.
To use the segment addition postulate, we need to find the length of segment BC.
The segment addition postulate states that if A is between B and C, then AB + BC = AC.
In this case, AB = BA = 7w - 12, and AC = 6w - 14. Substituting these values into the segment addition postulate, we get:
7w - 12 + BC = 6w - 14
To solve for BC, we need to isolate it on one side of the equation. We can do this by subtracting 7w and adding 12 to both sides of the equation:
7w - 7w - 12 + BC = 6w - 7w - 14 + 12
BC = -w - 2
Therefore, the length of segment BC is -w - 2.