if PQ || RS and the slope of PQ = x-1/4 and the slope of RS is 3/8 then find the value of x justify algebraically and numerically

The value of x is 5/8.

Step-by-step explanation:

Given,

The lines PQ and RS are parallel to each other. slope of PQ = x-1/4 slope of RS = 3/8

The slopes of parallel lines are equal.

slope of PQ = slope of RS

⇒ x-1/4 = 3/8

⇒ (4x-1) / 4 = 3/8

⇒ 8 (4x-1) = 4 (3)

⇒ 32x-8 = 12

⇒ 32x = 20

x = 20/32

x = 5/8