What are one-step subtraction equations (x - a = b)?

📚 What is a One-Step Subtraction Equation?

A one-step subtraction equation is an algebraic equation that can be solved in just one step using subtraction. It typically looks like this: $x - a = b$, where $x$ is the unknown variable we want to find, and $a$ and $b$ are known numbers.

📜 History and Background

The concept of solving equations dates back to ancient civilizations. Egyptians and Babylonians were solving linear equations as early as 1650 BC. Over time, mathematicians developed more sophisticated methods for solving various types of equations, leading to the algebraic techniques we use today. The one-step subtraction equation is a fundamental building block in algebra.

🔑 Key Principles

• ⚖️ The Golden Rule: Whatever you do to one side of the equation, you must do to the other side to maintain equality.
• 🎯 Isolate the Variable: The goal is to get the variable ($x$) by itself on one side of the equation.
• ➖ Inverse Operation: Use the inverse operation of subtraction, which is addition, to isolate the variable.

✍️ Solving One-Step Subtraction Equations

To solve an equation in the form $x - a = b$, add $a$ to both sides of the equation:

$x - a + a = b + a$

This simplifies to:

$x = b + a$

➕ Real-World Examples

Let's look at some examples:

1. Example 1: Solve $x - 5 = 12$

   Add 5 to both sides: $x - 5 + 5 = 12 + 5$

   So, $x = 17$

2. Example 2: Solve $y - 3 = 7$

   Add 3 to both sides: $y - 3 + 3 = 7 + 3$

   So, $y = 10$

3. Example 3: Solve $z - 10 = 20$

   Add 10 to both sides: $z - 10 + 10 = 20 + 10$

   So, $z = 30$

💡 Tips and Tricks

• ✔️ Always check your answer: Substitute your solution back into the original equation to make sure it's correct.
• ➕ Addition is your friend: Remember to add the same number to both sides.
• ✍️ Show your work: Writing out each step can help you avoid mistakes.

📝 Practice Quiz

Solve the following equations:

1. $x - 8 = 15$
2. $y - 2 = 9$
3. $z - 11 = 14$
4. $a - 6 = 24$
5. $b - 4 = 13$
6. $c - 9 = 16$
7. $d - 7 = 18$

Answers:

1. $x = 23$
2. $y = 11$
3. $z = 25$
4. $a = 30$
5. $b = 17$
6. $c = 25$
7. $d = 25$

🎯 Conclusion

One-step subtraction equations are a fundamental concept in algebra. By understanding the key principles and practicing regularly, you can master them with ease. Keep practicing, and you'll become a pro in no time!