Algebra Magic - Solving Two-Step Equations

Contributor: Marlene Vogel. Lesson ID: 10487

Abracadabra algebra! Magic math! If those words don't seem to go together, this lesson will use videos, card games, and riddles to teach the real-life secrets of solving two-step equations! Ta da!


Expressions and Equations, Pre-Algebra

learning style
personality style
Lion, Beaver
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

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Here is a Magic trick! Follow the instructions and then try to figure out how it is done! 

  1. Pick a single digit number. 
  2. Add 5 to your number. 
  3. Multiply your answer by 2. 
  4. Subtract 4. 
  5. Divide your answer by 2. 
  6. Subtract your original number. 
  7. Your answer is 3!

Today you will continue to practice your equation-solving skills and expanding on them by learning to solve two-step equations. When you were learning how to solve one-step equations you learned that you needed to use an operation opposite of the one in the equation to solve for an answer. When solving a two-step equation you will be working with two different operations and their opposites.  

Before trying to work out some problems, take a moment to watch this Algebra Basics: Solving 2-Step Equations-Math Antics video below. It will help you understand the process:

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Below is an example of how to solve a two-step equation: 

  1. The original equation is
    4x + 7 = 31                                                                      
  2. Remember, when solving the equation you want to get the variable on one side of the equals sign and the constant(s) or numbers on the other side of the equals sign. Also, remember that what you do to one side of the equation (equals sign) you must do to the other side.
  3. Subtract the 7 from both sides of the equation. 
    4x + 7 - 7 = 31 - 7 
    4x = 24 
  4. Divide both sides of the equation by 4 to get the variable (x) by itself.
    4x/4 - 24/4 
  5. On the left side of the equation, the 4 in the numerator and the 4 in the denominator cancel each other out and you are left with x. On the right side of the equation you can simplify the fraction to 6, because 24 divided by 4 equals 6. Your solution for the two-step equation is x = 6. Remember, the goal of solving an equation is to find the value of x. This 5-step process illustrates how to meet that goal.
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