The objective in solving any equation is to find the value or values of the variable terms which make the equation true. In general, the means by which we determine those values is first to isolate the variable by performing those operations necessary to get all the terms having the variable combined together, and then to provide the variable term with a coefficient of 1.

For example, let’s solve the equation . Subtract 3x from both sides, to place the variable terms on the right side, and subtract 4 from both sides, to move the numerical terms to the left side of the equation. Combining those terms, we have . Now divide both sides by 2, to isolate the variable term with a coefficient of 1, and our solution is . Checking our solution, we find that , so our solution is correct.

In our next topic, we will learn to solve algebraic equations containing variables and radical terms. In doing so will learn techniques for those types of equations which help us obtain our goal: to determine the values of the variable which makes the radical equation true.