You get the exact solution.
yes
It is the solution of the equation
It is important to check your answers to make sure that it doesn't give a zero denominator in the original equation. When we multiply both sides of an equation by the LCM the result might have solutions that are not solutions of the original equation. We have to check possible solutions in the original equation to make sure that the denominator does not equal zero. There is also the possibility that calculation errors were made in solving.
5R=45
You get the exact solution.
That's an extraneous solution. You need to check for these when algebraically solving equations, especially when you take both sides of an equation to a power.
yes
Yes it is quite possible
Methods vary considerably depending upon the number of powers in the equation. For example, the method for solving cubics is quite different to solving quadratics etc... It's not really possible to generalise to one technique.
What role of operations that applies when you are solving an equation does not apply when your solving an inequality?"
No because you always keep an equation in balance when solving it
It is the solution of the equation
Some operations cannot be done. For example, if we take the equation x=2/0, there is no result, because division by 0 is not defined.
Ask someone eles.
An equality and equation are essentially the same thing. The equality between two expressions is represented by an equation (and conversely).
An equation is a mathematical statement that may (or may not) be true, defined for some variables. Solving an equation is finding those values of the variables for which the equation or statement is true.