Lesson 6

Refresher

 

The basic rule used in solving equations in algebra is to balance both sides of the equation. In other words, what is done to one side of the equation must be done to the other side of the equation as well. For example, if you add a term on the left side, you must add the same term on the right side. If you multiply a term on the left side, you must multiply the same term on the right side. The following table shows how you can solve two different linear equations.

 

Solving a Basic Equation	Solving by Combining Like Terms
In the equation 6 = 3 − x, you want to get the x on the left side and the other items on the right side.   First, add x to both sides of the equation.     6 + x = 3 − x + x   6 + x = 3   Next, subtract 6 from both sides of the equation.       By following these two steps, you learn that x = −3, which is the solution to the equation.	Consider the equation 2x + 3 = −4x − 7.   You can solve the equation by first getting all the x-terms on the left side.   Add 4x to both sides.     2x + 4x + 3 = −4x + 4x − 7   Combine like terms.     6x + 3 = −7   Subtract 3 from both sides.     6x + 3 − 3 = −7 − 3   Combine like terms.     6x = −10   Divide both sides by 6.       Simplify the fraction.

 

Try the “Algebra Four!” equations game to practise your equation-solving skills. You can choose different types of questions to practise. Select “Two-Step Problems,” and then play one round. Next, you can add “Variable on Both Sides” the second time you play. This game is best played with two people, so you may want to invite a classmate to play with you, or perhaps your teacher or a parent may be willing to play with you. If you feel up to the challenge, you can select the first, second, and fourth options. (Do not select the “Quadratic” option, as you will be learning how to solve quadratic equations in a future course.) As a helpful hint, if you try the game, you may need to have a piece of paper and a pencil handy.

 

© Shodor

 

If you had trouble factoring the expressions, work through the Factoring Special Products gizmo.

 

Screenshot reprinted with permission of ExploreLearning.

 

Go back to the Are You Ready? section, and try the questions again. If you are still having difficulty, contact your teacher.