Let’s review the various techniques for solving algebraic equations containing variables:

• For linear equations in one variable, you may solve for that variable by first separating the variable and numerical terms, and then isolating the variable on one side of the equation to identify a single solution.
• When the linear equation has two variables, you may only solve for one of the variables in terms of the other (for example: the equation x - y = 3 may be solved for y in terms of x, y = x - 3, or x in terms of y, x = y + 3 . These equations have infinite solutions (points in the form (x,y) which solve the equation) and graph as lines.
• A quadratic equation has two solutions: two real solutions, one real duplicate solution, or two complex solutions, based on the value of the discriminant. Begin by placing the equation in its standard form and selecting an appropriate method (graphing, factoring, taking square roots, completing the square, or quadratic formula).
• A radical equation requires you to isolate and then square the radical term (or one of the radical terms if there are more than one) and then use algebra to solve for the linear variable.

In this topic, you will learn to solve a new type of equation, called rational equations. Let’s prepare for that by solving some more familiar types of equations. Click here to begin the self check.