Question

B is the midpoint of segment AC; AB = 8v, and AC = 2v + 42. What is BC?

Answer 1

2 * AB = AC  
2 * 8v = 2v + 42
16v - 2v = 42
14v = 42
v = 42/14
v = 3

BC = AB = 8v = 8*3 = 24

Answer 2

Segment BC is: 24

Given:

$AB = 8v\\AC = 2v + 42$

If B is the midpoint of segment AC, it implies that points A, B, and C are collinear.

Also:

$AB = BC$

Therefore:

$2(AB) = AC$

Substitute:

$2(8v) = 2v + 42$

Solve for v

$16v = 2v + 42$

Subtract 2v from both sides

$16v - 2v = 42\\14v = 42$

Divide both sides by 14

$v = 3$

Thus:

$AB = BC =8v$

Plug in the value of v

$BC = 8(3)\\BC = 24$

Therefore, segment BC is 24 units.

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