It does not matter which textbook your school has chosen to use, nor does it really matter the age of the text. Solving multi-step equations will be apart of what you have learned. I work with Prentice Hall's Algebra 1 (2009) and in the years before that I worked with Glencoe's Algebra 1 (1999). I tell you what books I have used because that should give you a clear picture that solving equations is an important part algebra and learning how to solve one-step equations is the building block to solving two-step and multi-step equations. Remember, the goal of solving multi-step equations is to isolate the variable correctly to get the answer.
Isolating the Variable
Solving One Step Equations with Addition and Subtraction
Example 2 is another equation in which the focus can be on the operation between the variable and the number. The focus can be on the the sign between the number and variable when the number is positive. As in example 2, since 6 is added to the variable, to get rid of the 6, it is subtracted from the 6 on the left and it is subtracted from the right to maintain the balance of the equation. Because the 6 and -6 on the left are opposites, those numbers combine to give 0 and the variable is isolated. Another way teachers will describe what happens on the left is to say "the 6's cancel".
Addition is Subtraction and Subtraction is Addition
What? This topic can be be very confusing if you are unaware of two facts:
- Adding a negative number is the same as subtracting a positive number
- Subtracting a negative number is the same as adding positive number
|Example 4 Incorrect and Correct Way To Solve an Equation|
If it is obvious to you that you need to add to solve this equation, then rewriting the equation as equation 2 is not necessary to find the correct solution.
The final example, rule #2 is illustrated. Equation 1 is x - (-5) = 7. Notice the "double negative" between the variable and the number. Some teachers, including will say, "a double negative makes a positive." We say that because it does and it offers an easy way to remember rule number 2. After using rule #2, the equation can be solve by subtracting 5 from both sides. This isolates the variable and gives x = 2.
Using the below video will give you some interactive practice with solving one-step equations with addition and subtraction.