Prove that between any two different real numbers there is a rational number and an irrational number

Rational Number is the combination of both rational and irrational number.

Thus, any two real number it can be rational and an irrational number..

Example: -3.12 is a real number but it is also rational

and 8.3333.... is also a real number but it is also an irrational number.

Further,

Rational Number is the number in the form , where q≠0.

Example:

Real Number is the all numbers including natural, whole, integers, rational, irrational number except the imaginary numbers.

Example: , 5, √28, etc.

The decimal which is non-terminating, non-repeating decimal expansion and thus it can't be written in the form of simple fraction is called irrational number.

Example: √5, π, 27.458978445...., etc.

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3