Decide whether a number is a solution of a linear
equation. If the variable in an equation can be replaced by a real number
that makes the statement true, then that number is a solution of the equation.
For example, 8 is a solution of the equation x – 3 = 5, since replacing x
with 8 gives a true statement, 8 – 3 = 5. An equation is solved by finding
its solution set, the set of all solutions. The solution set of the equation
x – 3 = 5 is {8}.
Equivalent equations are equations that have the same solution set. To
solve an equation, we usually start with the given equation and replace it
with a series of simpler equivalent equations. For example,
5x + 2 =17, 5x = 15, and x = 3 Â Equivalent equations
are all equivalent since each has the solution set {3}.