Answer:
[tex] x = 9 [/tex]
Step-by-step explanation:
Given:
[tex] PQ = x - 5 [/tex]
[tex] QR = 2x - 1 [/tex]
[tex] PR = 21 [/tex]
Required:
Value of x
SOLUTION:
Point P, Q, and R are collinear, therefore:
[tex] PQ + QR = PR [/tex] (segment addition postulate)
[tex] (x - 5) + (2x - 1) = 21 [/tex] (substitution)
Solve for the value of x using the above equation.
[tex] x - 5 + 2x - 1 = 21 [/tex]
Combine like terms
[tex] x + 2x - 5 - 1 = 21 [/tex]
[tex] 3x - 6 = 21 [/tex]
Add 6 to each side of the equation
[tex] 3x - 6 + 6 = 21 + 6 [/tex]
[tex] 3x = 27 [/tex]
Divide each side by 3
[tex] \frac{3x}{3} = \frac{27}{3} [/tex]
[tex] x = 9 [/tex]
