A, B, and C are collinear and B is between A and C. If AB= 3x+3, BC=6x+1, and AC=7x+14. What is x?

Answer 1

Sine they are collinear, we know: Segment 1 + Segment 2 = Total length

Since B is between A and C, we can set up the following equation: AB+BC=AC

(3x+3)+(6x+1) = 7x+14 Not we can solve this. Combine like terms

9x+4 = 7x+14 Subtract 7x from both sides

9x+4-7x = 7x+14-7x Simplify

2x+4 = 14 Subtract 4 from both sides

2x+4-4 = 14-4

2x = 10 Divide both sides by 2

x=5

Answer 2

It is always a good idea to check your work. Suppose the answer determined is x=5.

[ 3x + 3 ] + [ 6x + 1 ] = 7x + 14

Substituting 5 for x,

[ 3 * (5) + 3 ] + [ 6 * (5) + 1] = 7 * (5) + 14

[ 15 + 3 ] + [ 30 + 1] = 35 + 14

[ 18 ] + [ 31 ] = 49

49 = 49

Which verifies the solution. It is all too easy to make a mistake and find the right answer to the wrong problem.

Checking your answer shows you are willing to make sure you have determined the correct solution.