A certain fraction becomes equal to 1/2
when 1 is subtracted from its
numerator and 1 is added to its denominator. Also, it becomes 1/3
when 6 is subtracted from its numerator and 1 from the denominator.
Find the original fraction.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

cross multiplying, we get :

⇒ (3) × (5) = (9) × (x)

⇒ 15 = 9x