An equation is a mathematical sentence that asserts that two expressions are equivalent.

The equals sign (=) is used to indicate the equivalence of the two expressions.

Example:  5 + 2 = 14 / 2

Both expressions represent the value 7 so are equivalent.

In algebra, we are often asked to find a missing variable that would give us equality; we are solving the equation, which means we find the value(s) of the missing variable that make the equation true.

For example, find x that makes the equation true:  2x + 4 = 10

We use the properties of equality to help us find the solution to this equation, that is, the value(s) of x that make it true.  In this case, we would solve as shown below:

2x + 4 = 10                (Original equation)

2x + 4 - 4 = 10 - 4      (Subtraction property of equality)

2x = 6                        (Simplify)

2x/2 = 6/2                  (Division property of equality)

x = 3

(Check the solution is correct by plugging 3 back into the original equation:  2(3) + 4 = 10; 6 + 4 = 10; 10 = 10)

For equations such as the one above, there is one solution.  Sometimes there can be more than one solution to an equation.

For example, find the solution to x² = 4.

There are two solutions:  2 and -2.

Linear equations are equations that when graphed will form a line.  Quadratic equations form curves; we will discuss the parabolas formed by quadratic equations.

We can also solve for a variable when presented with an equation.