If b is the midpoint of line AC, and AC = 8x-20, find BC.

The Definition Of a Midpoint says that is B is the

midpoint of segment AC, then segment AB ≅ AC.

Since segment AB ≅ segment BC, we can setup

the equation 2(3x - 1) = 8x - 20 and we can solve from here.

Start by distributing the 3 through the parenthses on the left side.

So we get 6x - 2 = 8x - 20.

Now subtract 8x from both sides to get -2x - 2 = -20.

Now add 2 to both sides and we have -2x = -18.

Finally, dividing both sides by -2, we find that x = 9.

If x = 9, segment BC must be 3(9) - 1 or 27 - 1 which is 26.

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