B is the midpoint of AC. AB = 3x + 4 and BC = 2x + 12. whats the length of bc and the value of x

Answer 1

Hi Alex,

This is an algebraic proof. Because B is the midpoint that means the length of AB is going to be equal to the length of BC by the definition of midpoint. Since this is the case (AB=BC) we can put our expressions equal to each other and solve for x.

3x + 4 = 2x + 12

-4 -4 Subtraction Property of Equality

3x = 2x + 8

-2x -2x Subtraction Property of Equality

x = 8

So your answer for x is 8

8 is the value of x so now you can find the length of BC. Here you would substitute your x into the expression 2x+12 or 2(8) + 12 which equals 28. This means 28 is the length of BC.

Hope this helps.

Answer 2

Since B is the midpoint of AC that means that it divide AC in two equal parts AB and BC. Translate them into an equation you have

3x+4=2x+12

Solving for x:

3x+4-4=2x+12-4 (subtract 4 from both sides)

3x=2x+8

3x-2x=8 (separate unknown from rest)

x=8

so

AB=3•8+4=28

BC=2•8+12=28