Question

Segment Addition Postulate: If PQ = x - 5, QR = 2x - 1, and PR = 21, find x. 3 points

Р
Q
R
D
17
Not enough information

Answer 1

`x = 9`

Explanation:

Given:

`PQ = x - 5`

`QR = 2x - 1`

`PR = 21`

Required:

Value of x

SOLUTION:

Point P, Q, and R are collinear, therefore:

`PQ + QR = PR` (segment addition postulate)

`(x - 5) + (2x - 1) = 21` (substitution)

Solve for the value of x using the above equation.

`x - 5 + 2x - 1 = 21`

Combine like terms

`x + 2x - 5 - 1 = 21`

`3x - 6 = 21`

Add 6 to each side of the equation

`3x - 6 + 6 = 21 + 6`

`3x = 27`

Divide each side by 3

`(3x)/(3) = (27)/(3)`

`x = 9`