Point J is on line segment IK . Given IK = 5x, IJ = 4 and JK = 4x determine the numerical length of IK.

IJ = 3x - 5

JK = 2x - 1

IK = 3x + 2

  IJ   +    JK   =    IK           segment addition postulate

3x - 5 + 2x - 1 = 3x + 2       substitution

           5x - 6 = 3x + 2       simplify (add like terms)

           2x - 6 = 2             subtraction property (subtracted 3x from both sides)

                 2x = 8             addition property (added 6 to both sides)

                   x = 4             division property (divided both sides by 2)

JK = 2x - 1   = 2(4) - 1   = 8 - 1   = 7

JK = 7

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.

one set of data has more variation than the other. hope this !