Point T is on a line segment SU. Given SU=4x+1, TU=3x, and ST=3x-1, determine the numerical length of SU

Answer 1

By the segment addition rule, length of ST + length TU equals length of SU so

3x -1 + 3x = 4x + 1

6x - 1 = 4x + 1

2x = 2

x = 1

substituting value of x back into formula for length of SU: 4(1) + 1 = 5

Answer 2

Since T is on segment SU we know the whole is eqaul to the sum of it’s parts.

ST + TU = SU substitute

3x - 1 + 3x = 4x + 1 simplify

6x - 1 = 4x + 1 solve for x

2x = 2

x = 1

ST = 3(1) -1 = 2

TU = 3(1) = 3

SU = 4(1) + 1 = 5