#7) M is the Midpoint of JK. Since there is no segment through M, then there is no segment bisector.
JM = 7x + 5, MK = 8x (Given)
JM ≡ MK (definition of midpoint)
JM = MK (definition of congruency)
7x + 5 = 8x (substitution)
5 = x (subtraction property of equality)
JM = 7x + 5 → JM = 7(5) + 5 → JM = 35 + 5 → JM = 40
#8) M is the Midpoint of JK. the line passing through M is line <em>l</em>, so line <em>l</em> is the segment bisector.
JM = 3x + 15, MK = 8x + 25 (Given)
JM ≡ MK (definition of midpoint)
JM = MK (definition of congruency)
3x + 15 = 8x + 25 (substitution)
15 = 5x + 25 (subtraction property of equality - subtracted 3x)
-10 = 5x (subtraction property of equality - subtracted 25)
-2 = x (division property of equality)
JM = 3x + 15 → JM = 3(-2) + 15 → JM = -6 + 15 → JM = 9
