Easy Method to Solve One-Step Equations (Addition Property of Equality)

📚 Understanding One-Step Equations (Addition Property of Equality)

A one-step equation involving addition is an algebraic equation that can be solved in just one step using the addition property of equality. This property states that adding the same number to both sides of an equation maintains the equality.

📜 History and Background

The concept of equality and manipulating equations has ancient roots, dating back to early civilizations like the Babylonians and Egyptians. However, the formalization of algebraic principles, including the addition property of equality, developed more extensively during the Islamic Golden Age and later in Europe with the work of mathematicians like Al-Khwarizmi and Robert Recorde.

🔑 Key Principles

• ➕Isolate the Variable: The goal is to get the variable alone on one side of the equation.
• ⚖️Addition Property of Equality: If $a = b$, then $a + c = b + c$. This means you can add the same value to both sides without changing the solution.
• ➖Use the Inverse Operation: To undo addition, use subtraction. If you have $x + a = b$, subtract $a$ from both sides: $x + a - a = b - a$, which simplifies to $x = b - a$.

✍️ Step-by-Step Solution

1. Identify the equation: Recognize the equation as a one-step addition equation (e.g., $x + 5 = 12$).
2. Isolate the variable: Subtract the number being added to the variable from both sides of the equation.
3. Simplify: Perform the subtraction to find the value of the variable.

➗ Real-World Examples

Example 1:

Solve for $x$ in the equation $x + 3 = 7$.

1. Original Equation: $x + 3 = 7$
2. Subtract 3 from both sides: $x + 3 - 3 = 7 - 3$
3. Simplify: $x = 4$

Example 2:

Solve for $y$ in the equation $y + 10 = 25$.

1. Original Equation: $y + 10 = 25$
2. Subtract 10 from both sides: $y + 10 - 10 = 25 - 10$
3. Simplify: $y = 15$

Example 3:

Solve: $a + 6 = 13$

1. Original Equation: $a + 6 = 13$
2. Subtract 6 from both sides: $a + 6 - 6 = 13 - 6$
3. Simplify: $a = 7$

💡 Practice Quiz

Solve the following equations:

1. $x + 4 = 9$
2. $y + 7 = 15$
3. $z + 2 = 11$
4. $a + 1 = 6$
5. $b + 8 = 12$
6. $c + 3 = 10$
7. $d + 5 = 14$

✅ Solutions to Practice Quiz

1. $x = 5$
2. $y = 8$
3. $z = 9$
4. $a = 5$
5. $b = 4$
6. $c = 7$
7. $d = 9$

🎯 Conclusion

The addition property of equality provides a straightforward method for solving one-step equations involving addition. By adding the same value to both sides of the equation, you can isolate the variable and find its value. This fundamental principle is a cornerstone of algebra and is essential for solving more complex equations.