Algebra Basics: Solving 2-Step Equations - Math Antics
Table of Contents
Introduction
This tutorial provides a clear, step-by-step guide to solving 2-step algebra equations. These equations typically involve one addition or subtraction operation and one multiplication or division operation. Understanding how to solve these equations is essential for mastering algebra, and this guide will help you build a strong foundation in solving them.
Step 1: Identify the Equation
- Start by writing down the equation clearly. For example:
- ( 2x + 4 = 12 )
- Identify the operations present in the equation (addition/subtraction and multiplication/division).
- Recognize the goal: isolate the variable (in this case, ( x )) on one side of the equation.
Step 2: Undo Addition or Subtraction
- Begin by eliminating any addition or subtraction from the equation.
- If the equation is ( 2x + 4 = 12 ):
- Subtract 4 from both sides to isolate the term with the variable.
- The equation now looks like this:
- ( 2x + 4 - 4 = 12 - 4 )
- Simplifies to ( 2x = 8 )
- Practical Tip: Always perform the same operation on both sides of the equation to maintain equality.
Step 3: Undo Multiplication or Division
- Next, tackle the multiplication or division to isolate the variable completely.
- Using our example ( 2x = 8 ):
- Divide both sides by 2:
- ( \frac{2x}{2} = \frac{8}{2} )
- This simplifies to ( x = 4 )
- Divide both sides by 2:
- Common Pitfall: Ensure you are performing the correct operation (divide if multiplied, and vice versa).
Step 4: Verify Your Solution
- It's crucial to check your work to ensure the solution is correct.
- Substitute ( x ) back into the original equation:
- ( 2(4) + 4 = 12 )
- Check if ( 8 + 4 = 12 )
- Since both sides are equal, the solution ( x = 4 ) is confirmed.
Conclusion
In this tutorial, you learned how to solve 2-step algebra equations by first undoing addition or subtraction and then addressing multiplication or division. Remember to always check your work by substituting your solution back into the original equation. Practicing these steps will help you become more confident in solving algebraic equations. For further practice, explore additional algebra resources or tackle more complex equations as your skills improve.