Find X and line segment BC if B is between A and C, line segment AC= 4x-12, and line segment BC = 2x+3

Question

Find X and line segment BC if B is between A and C, line segment AC= 4x-12, and line segment BC = 2x+3

Answer 1

Use this equation.

 

AB + BC = AC

 

AB + 2x + 3 = 4x - 12

 

 

Solving for x,

 

2x - 4x = -12 - 3 - AB

 

-2x = -15 - AB

 

   x = (-15 - AB) / -2

 

 

Plug in this value of x into the line segments to find BC and AC.

 

BC = 2[(-15 - AB) / -2] + 3

BC = -(-15 - AB) + 3

BC = AB + 18

 

AC = 4[(-15 - AB) / -2)] - 12

AC = -2(-15 - AB) - 12

AC = 30 + 2AB - 12

AC = 2AB + 18

 

 

Makes sense to you?  You did not specify an expression for AB, but this is how you would solve it in general.  I guess you will fill in that gap yourself.