What equation cannot be solved and why?
4 = 5
3x-7 = 3x+5
any two quantities which will always be different can surely not be set equal.
If there's something else you're after, try and be a bit clearer.
4 does not equal 5, and x=4.
An equation that cannot be solved is one that doesn't have a solution. This occurs when there is no value for the variable that will make the equation true. There are several reasons why an equation cannot be solved:
1. Inconsistent equations: If you have a system of equations that contradict each other, such as "x = 5" and "x = 7," there is no value that can satisfy both equations simultaneously. In this case, the system of equations is said to be inconsistent and has no solution.
2. Impossible equations: Some equations involve mathematical operations that lead to impossible or undefined results. For example, the equation "x = 1/0" is undefined because division by zero is undefined in mathematics. Similarly, the equation "√x = -4" has no solution because square roots of real numbers are non-negative.
3. Overdetermined systems: In some cases, you may have more equations than variables in a system. If the equations are not dependent on each other, it is possible that no solution exists. For example, having three equations and two variables can lead to an overdetermined system with no solution unless one equation can be derived from the other two.
4. Non-algebraic equations: There are types of equations that cannot be solved using algebraic methods alone, such as transcendental equations, which involve exponential, logarithmic, or trigonometric functions. These equations often require numerical or approximation techniques to find an approximate solution.
In summary, equations that cannot be solved either have no solution due to inconsistencies or impossibilities, or they require techniques beyond algebra to find a solution.