The equations with no real numbers for solutions may have the same varibles on each side

of the equation, but are different by some number or operations.

Consider the equation .

The equation wiill have no solution, since  can never equal .

Equations that have all of the real numbers as solutions are equations with th

same variable and same numbers and operations on both sides of the equation.

For example, or have all real numbers as their solutions

since the left side of the equation will always equal the right for any value of .