How do you know when an equation has no solution or when it is an identity?

Answer 1

Well, sweetheart, when you solve an equation and you end up with a contradiction like "1 = 0," that's a dead giveaway that there's no solution. On the other hand, if you solve an equation and you get a true statement like "3 = 3," then you've got yourself an identity. It's as simple as that, sugar.

Answer 2

Oh, dude, it's like when you're solving an equation and you end up with something ridiculous like 2 = 3. That's when you know it's got no solution. And if you simplify both sides and they end up being the same no matter what, like 2x = 2x, then congrats, you've got yourself an identity. It's like solving a puzzle, but with more math and less fun.

Answer 3

Well, isn't that just a happy little question! When you're working with equations, if you find that both sides of the equation simplify to the same expression, then you've got yourself an identity. On the other hand, if you reach a point where the equation leads to a contradiction, like 3 = 5, then there's no solution to be found. Just trust your instincts and keep painting those math problems with joy and curiosity!

Answer 4

There is no simple way which can be easily applied to all forms of equations. If the variable(s) can be eliminated from the equation then, if what is left is

• false, then the equation has no solution.
  
• true, then the equation is an identity.

The problem is complicated by the domains under consideration. The following are some examples of equations which have no solutions in one domain but do in another [larger] domain:

• x + 2 = 0 has no solution in N (natural numbers) but does in Z (integers)
  
• x*2 = 1 has no solution in Z but does in Q (rational numbers)
• X^2 = 2 has no solution in Q but does in R (real numbers)
• x^2 = - 2 has no solution in R but does in C (complex numbers).

Answer 5

You may need to actually solve the equation.