Question

Solve for x given BD = 4x+3 and AE = 4x+8. Assume B is the midpoint of segment AC and D is the midpoint of segment CE.

Answer 1

Answer: The fraction x = 1/2 or its equivalent decimal form x = 0.5

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Work Shown:

AE = 2*(BD)

4x+8 = 2*(4x+3)

4x+8 = 8x+6

8-6 = 8x-4x

2 = 4x

4x = 2

x = 2/4

x = 1/2

x = 0.5

note: the first equation is set up basically saying that AE is twice that of BD; put another way, BD is half as long as AE. This is one property of midsegments. Another property is that AE and BD are parallel.

another note: if x = 0.5, then AE = 4*x+8 = 4*0.5+8 = 10 while BD = 4*x+3 = 4*0.5+3 = 5, showing that AE is indeed two times longer than BD.