Question

B is the midpoint of AC. If: AB = 9x+1 and BC= 6x+25 Find AC

Answer 1

146

Explanation:

AB = BC (Definition of midpoint) so:

9x+1=6x+25.

Solve it as you would any other algebraic equation >>> 9x+1=6x+25 >>> 9x+1-1=6x+25-1 >>> 9x=6x+24 >>> -6x+9x=6x-6x+24 >>> 3x=24 >>> 3x/3=24/3 >>> x=8

AB=9x+1 >>> AB=9*8+1 >>> AB=73

BC=6x+25 >>> BC=6*8+25 >>> BC=73

AC=AB+BC >>> AC=73+73 >>> AC=146

Answer 2

AC = 146

Explanation:

Given that B is the midpoint of AC, then

AB = BC, that is

9x + 1 = 6x + 25 ( subtract 6x from both sides )

3x + 1 = 25 ( subtract 1 from both sides )

3x = 24 ( divide both sides by 3 )

x = 8

Hence

AC = AB + BC = 9x + 1 + 6x + 25 = 15x + 26, thus

AC = (15 × 8) + 26 = 120 + 26 = 146