Question

Suppose PR = 54, solve for QR
4x-1
3x-1
P
R

Answer 1

`QR = 23`

Explanation:

P, A, and R are collinear.

PR = 54

`PQ = 4x - 1`

`QR = 3x - 1`

To solve for the numerical length of PR, let's generate an equation to find the value of x.

According to the segment addition postulate:

`PQ + QR = PR`

`(4x - 1) + (3x - 1) = 54` (substitution)

Solve for x

`4x - 1 + 3x - 1 = 54`

Combine like terms

`4x + 3x - 1 - 1 = 54`

`7x - 2 = 54`

Add 2 to both sides

`7x - 2 + 2 = 54 + 2`

`7x = 56`

Divide both sides by 7

`(7x)/(7) = (56)/(7)`

`x = 8`

`QR = 3x - 1`

Plug in the value of x into the equation

`QR = 3(8) - 1 = 24 - 1`

`QR = 23`