AC = 23. AB = 2x + 2, and BC = 3x + 6. Find BC

Step-by-step explanation:

Given AC = 23, AB = 2x + 2 and BC = 3x+6 then using vector notation;

BA+AC = BC

Since BA = -AB

The equation becomes -AB+AC = BC

Substituting the given equations;

-(2x+2)+23 = 3x+6

open the parenthesis

-2x-2+23 = 3x+6

-2x+21 = 3x+6

collect the like terms

-2x-3x = 6 - 21

-5x = -15

Divide both sides by -5

-5x/-5 = -15/-5

x = 3

TO get BC, we will substitute x = 3 into the expression BC = 3x+6

BC = 3(5)+6

BC = 15+6

BC = 21

Hence the length of BC is 21 units

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