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AB is 104

Step-by-step explanation:

In the given figure

∵ CE bisects the segment AB

→ That means CE intersects AB at the midpoint of AB

∵ CE ∩ AB at point F

∴ F is the midpoint of AB

→ The midpoint of a segment divides it into two equal parts

∵ The point F divides AB to FA and FB

∴ FA = FB

∵ FA = 7x + 10

∵ FB = 9x - 2

→ Equate them

∴ 9x - 2 = 7x + 10

→ Add 2 to both sides

∵ 9x - 2 + 2 = 7x + 10 + 2

∴ 9x = 7x + 12

→ Subtract 7x from both sides

∵ 9x - 7x = 7x - 7x + 12

∴ 2x = 12

→ Divide both sides by 2

∴ x = 6

→ Substitute the value of x in FA and FB

∵ FA = 7(6) + 10 = 42 + 10 = 52

∵ FB = 9(6) - 2 = 54 - 2 = 52

∵ AB = FA + FB

∴ AB = 52 + 52 = 104

∴ AB = 104