How can you find a solution to an equation with a variable?

Answer 1

The answer depends on the nature of the equation. Some equations can be solved by analytical methods. For example, you can carry out the basic operations of arithmetic on both sides of the equation so as to isolate the variable. Isolating the variable means that only the variable appears on one side of the equation and the other side contains only arithmetic expressions which can be evaluated.

For example, if the equation is 3x + 5 = 7

then subtracting 5 from both sides gives 3x = 2

and dividing both sides by 3 gives x = 2/3.

Some equations cannot be solved in this way. Sometimes there are formulae - such as the quadratic formula - while at other times the only option is to use numerical methods (trial and improvement or its more sophisticated versions).

Answer 2

Depending on the type of equation, this can be very simple or very complicated. The basic procedure is shown, with many example, in any high school algebra textbook. The main idea (for the simpler cases) is to do the same operation on both sides of the equation, until the variable is alone on one side. Here is an example:2x + 5 = 25

The objective is to have the "x" alone. One way of going in this direction is to subtract 5 from both sides, to get rid of the 5:

2x + 5 - 5 = 25 - 5

or:

2x = 20

Next, you need to get rid of the 2 (your objective is still to have the "x" alone on the left):

2x/2 = 20/2

or: (2/2)x = 10

or: x = 10