Question

given pq = 2x and qr = 4x - 8 and pr = 16. what is the value of x? what is the value of pq? what is the value of qr?

Answer 1

Answer:
X= 4
PQ= 8
QR= 8

Explanation:
As shown in the diagram, the line PR is made of the lines PQ and QR. Therefore, we can assume the equation PQ+QR=PR. When using the given values in the problem and substituting them in our equation, it becomes: 2X+4X-8=16 because PQ=2X, QR=4X-8, and PR=16. Here is how x is solved for:
2X+4X-8=16 (Original equation)
6X-8=16 (Simplify by adding 2X and 4X together)
6X=24 (Add 8 to both sides to isolate X)
X=4 (Divide both sides by 6, singling X out)
Referring back to how PQ=2X and QR=4X-8 we can solve for the each now that we know the value of X.
X=4
PQ= 2X= 2*4= 8
QR= 4X-8= 4(4)-8= 16-8=8
Additionally, we can check the answer by seeing if PQ and QR add to make the value of PR, which is given as 16. This proves to be correct as 8+8=16.
**Btw the diagram is not always going to look aligned to the values of the problem. Even though Q is not centered at the midpoint, PQ and QR are equal in value. Diagrams can be deceiving if not specified as to scale!**