๐ Understanding One-Step Subtraction Equations
A one-step subtraction equation is an algebraic equation that can be solved in just one step by using the inverse operation of subtraction, which is addition. The goal is to isolate the variable (usually represented by a letter like $x$, $y$, or $z$) on one side of the equation.
๐ History and Background
The concept of solving equations dates back to ancient civilizations. Egyptians and Babylonians used methods to solve mathematical problems, but the symbolic notation we use today developed gradually through the work of mathematicians over centuries. The use of variables and systematic methods for solving equations became more refined during the Renaissance and the early modern period.
๐ Key Principles for Solving
- โ๏ธ The Golden Rule: What you do to one side of the equation, you must do to the other. This maintains the balance and ensures the equation remains true.
- โ Inverse Operation: To isolate the variable in a subtraction equation, use addition. Adding the same number to both sides cancels out the subtraction.
- ๐ฏ Isolate the Variable: The ultimate goal is to get the variable by itself on one side of the equation. This tells you the value of the variable.
โ๏ธ Step-by-Step Guide
- Identify the Equation: Recognize the equation as a one-step subtraction equation. For example: $x - 5 = 12$.
- Apply Addition: Add the number being subtracted from the variable to both sides of the equation. In the example above, add $5$ to both sides: $x - 5 + 5 = 12 + 5$.
- Simplify: Simplify both sides of the equation. In our example, this becomes $x = 17$.
- Check Your Solution: Substitute the value you found for the variable back into the original equation to make sure it holds true. $17 - 5 = 12$, which is correct!
โ Real-World Examples
- ๐ Example 1: Sarah had a bag of apples. She gave 3 apples to her friend, and now she has 7 apples left. How many apples did she start with? Equation: $x - 3 = 7$. Solution: $x = 10$. Sarah started with 10 apples.
- ๐งธ Example 2: A toy store sold 15 teddy bears in the morning. In the afternoon, they had 22 teddy bears remaining. How many teddy bears did they have at the start of the day? Equation: $y - 15 = 22$. Solution: $y = 37$. The store started with 37 teddy bears.
- ๐ Example 3: A baker used 8 cups of flour for a cake. He had 4 cups of flour left. How many cups of flour did he have before baking? Equation: $z - 8 = 4$. Solution: $z = 12$. The baker initially had 12 cups of flour.
๐ก Tips and Tricks
- โ
Double-Check: Always substitute your answer back into the original equation to verify it.
- ๐ Write Neatly: Keep your work organized to avoid mistakes.
- ๐ค Practice Regularly: The more you practice, the easier it becomes!
โ Practice Quiz
| Question |
Equation |
Solution |
| 1 |
$x - 10 = 5$ |
$x = 15$ |
| 2 |
$y - 3 = 11$ |
$y = 14$ |
| 3 |
$z - 7 = 20$ |
$z = 27$ |
| 4 |
$a - 1 = 9$ |
$a = 10$ |
| 5 |
$b - 12 = 6$ |
$b = 18$ |
| 6 |
$c - 4 = 8$ |
$c = 12$ |
| 7 |
$d - 9 = 1$ |
$d = 10$ |
๐ฏ Conclusion
Solving one-step subtraction equations is a fundamental skill in algebra. By understanding the key principles and practicing regularly, you can master this concept and build a strong foundation for more advanced math topics. Keep practicing, and you'll become a subtraction equation solving pro in no time!