How to solve one-step equations with addition: A step-by-step guide

📚 What is a One-Step Equation with Addition?

A one-step equation with addition is an algebraic equation that can be solved in just one step by using the inverse operation of addition, which is subtraction. The goal is to isolate the variable (usually represented by letters like $x$, $y$, or $z$) on one side of the equation to find its value.

📜 History and Background

The concept of solving equations dates back to ancient civilizations, with early forms of algebra appearing in Babylonian and Egyptian mathematics. The formalization of algebraic notation and methods for solving equations evolved over centuries, with significant contributions from mathematicians in the Islamic world and later in Europe. While the idea of manipulating equations to isolate unknowns is ancient, the explicit and systematic approach to solving one-step equations is a core part of modern algebra education.

🔑 Key Principles for Solving One-Step Equations with Addition

• ⚖️ The Golden Rule: Whatever you do to one side of the equation, you must do to the other side to maintain equality.
• ➕ Identify the Operation: In this case, it's addition. Determine what number is being added to the variable.
• ➖ Use the Inverse Operation: Apply subtraction to both sides of the equation to isolate the variable.
• ✅ Check Your Solution: Substitute the value you found for the variable back into the original equation to ensure it makes the equation true.

🚶 Step-by-Step Guide with Examples

Let's walk through solving a one-step equation with addition:

Example 1: Solve for $x$ in the equation $x + 5 = 12$

1. ➕ Identify the number being added to $x$: It's 5.
2. ➖ Subtract 5 from both sides of the equation: $x + 5 - 5 = 12 - 5$
3. Simplify: $x = 7$
4. ✅ Check your solution: $7 + 5 = 12$. This is true, so $x = 7$ is correct.

Example 2: Solve for $y$ in the equation $y + 3 = 8$

1. ➕ Identify the number being added to $y$: It's 3.
2. ➖ Subtract 3 from both sides of the equation: $y + 3 - 3 = 8 - 3$
3. Simplify: $y = 5$
4. ✅ Check your solution: $5 + 3 = 8$. This is true, so $y = 5$ is correct.

Example 3: Solve for $z$ in the equation $z + 10 = 15$

1. ➕ Identify the number being added to $z$: It's 10.
2. ➖ Subtract 10 from both sides of the equation: $z + 10 - 10 = 15 - 10$
3. Simplify: $z = 5$
4. ✅ Check your solution: $5 + 10 = 15$. This is true, so $z = 5$ is correct.

✍️ Practice Quiz

Solve each equation for the variable:

1. $a + 4 = 9$
2. $b + 7 = 11$
3. $c + 2 = 6$
4. $d + 6 = 14$
5. $e + 1 = 10$
6. $f + 8 = 15$
7. $g + 3 = 12$

Answers:

1. $a = 5$
2. $b = 4$
3. $c = 4$
4. $d = 8$
5. $e = 9$
6. $f = 7$
7. $g = 9$

💡 Tips and Tricks

• 🎯 Focus on Isolating the Variable: Always aim to get the variable alone on one side of the equation.
• 🔢 Double-Check Your Arithmetic: Make sure your addition and subtraction are correct to avoid errors.
• ✍️ Show Your Work: Writing out each step can help you catch mistakes and understand the process better.

🌍 Real-World Applications

One-step equations with addition are used in various real-world scenarios, such as:

• 💰 Budgeting: Calculating how much more money you need to reach a savings goal.
• 📏 Measurement: Determining an unknown length when you know the total length and a part of it.
• 🌡️ Temperature: Figuring out the initial temperature if you know the final temperature and the increase.

🎓 Conclusion

Solving one-step equations with addition is a fundamental skill in algebra. By understanding the key principles and practicing regularly, you can master this concept and build a solid foundation for more advanced mathematical topics. Keep practicing, and you'll become a one-step equation solving pro! 👍