With mathematical connections write an expression for the length of the segment

PR = 13y +25

QR = 5y+20

Step-by-step explanation:

For figure a.

AB = x+2

BC = 7x-3

AC and AB + BC coincides with each other, so they should be equal

i.e AC = AB + BC

{ We know that things which coincide with each other are equal }

Therefore,

AC = AB + BC = ( x+2 ) + ( 7x-3 ) = x+2+7x-3 = 8x-1

For figure b.

PQ = 8y + 5

PR = 13y +25

PR and PQ + QR coincides with each other , so they should be equal

i.e PR = PQ + QR

{ We know that things which coincide with each other are equal }

Therefore,

PR = PQ + QR

QR = PR - PQ

QR = ( 13y +25 ) - ( 8y + 5 )

QR = 13y+25-8y-5

QR = 5y+20

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x