Question

T is the midpoint of AE. AT=4x-3 and TE= 2x+7, find the length of AE

Answer 1

If T is the midpoint, then that means its exactly 1/2 of the way between 2 points

this means we can set the 2 given values equal

4x - 3 = 2x + 7

first move like terms to the same side

2x = 10

x = 5

now that we know the length of x, we plug it back in to get the length

4x - 3 + 2x + 7 = 6x + 4

6(5) + 4 = 34