The denominator of a rational number is greater than its numerator by 10. if the
numerator is increased by 19 and the denominator is decreased by 1. the number obtained is 3/2. find the original number.

The denominator of a rational number is greater than its numerator by 10. The required rational number is

Solution:

Let the numerator be x.

And, denominator = x + 10

hence the original fraction is

Given that numerator is increased by 19 and denominator is decreased by 1 then the fraction is equal to

Evaluate the above expression

2(x+19)=3(x+9)  

Multiply 2 with (x+19) and Multiply 3 with (x+9)

2x+38=3x+27

Keep x in one side and constant in other side. so that we can find the value of x.

2x-3x=27-38

-x= -11

Eliminating the ‘-‘sign

Therefore x=11.

Hence, required fraction =  

Hence the required number is

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is