an equation with no solution is true false or identity
An equation with no solution is false.
An equation with no solution is considered false.
An equation with no solution is "false."
To understand why, let's first explore the three types of equations:
1. True Equation: An equation that is true for all values of the variables. For example, 2 + 3 = 5 is a true equation because it holds true regardless of the values chosen for the variables.
2. False Equation: An equation that is false for all values of the variables. For example, 2 + 3 = 8 is a false equation because it never holds true for any values of the variables.
3. Identity Equation: An equation that is true for some values of the variables but not others. For example, x + 2 = x + 2 is an identity equation since it is true for any value of "x."
Now, considering an equation with no solution, it falls under the category of a "false equation." This means that no matter what values you substitute for the variables, the equation will never be true. In other words, there is no solution that can satisfy the equation.
For instance, if we have an equation like 2x + 5 = 2x + 7, we can subtract 2x from both sides and simplify it to 5 = 7, which is clearly false. Thus, there is no solution that can make this equation true. Therefore, an equation with no solution is "false."