How to solve one-step multiplication equations (ax=b) for beginners

📚 Understanding One-Step Multiplication Equations

One-step multiplication equations are algebraic equations that can be solved in, you guessed it, one step! They usually look like this: $ax = b$, where 'a' and 'b' are numbers, and 'x' is the unknown variable we want to find.

📜 A Little History

The history of algebra dates back to ancient civilizations like the Babylonians and Egyptians, who developed methods for solving linear equations. However, the symbolic notation we use today evolved gradually over centuries, with significant contributions from mathematicians like Muhammad al-Khwarizmi.

🔑 The Key Principle: Inverse Operations

The core idea is to isolate the variable 'x' by performing the inverse operation. Since 'x' is being multiplied by 'a', we need to do the opposite: divide both sides of the equation by 'a'.

• ➗The Division Property of Equality: If you divide both sides of an equation by the same non-zero number, the equation remains balanced.
• 🎯Isolating the Variable: Our goal is always to get 'x' by itself on one side of the equation.
• 🧮General Formula: To solve $ax = b$, divide both sides by 'a': $x = \frac{b}{a}$

✍️ Step-by-Step Solution

Let's take the equation $3x = 12$ as an example:

1. Identify 'a' and 'b': In this case, $a = 3$ and $b = 12$.
2. Divide both sides by 'a': $\rac{3x}{3} = \rac{12}{3}$
3. Simplify: $x = 4$

🌍 Real-World Examples

One-step multiplication equations pop up everywhere! Here are a few scenarios:

• 🍕Splitting the Pizza: If 4 friends want to split a pizza ($p$) evenly, the equation is $4x = p$, where x is each person's share.
• 🛍️Buying Multiple Items: If each candy bar ($c$) costs $2 and you spent $10, the equation is $2x = 10$, where x is the number of candy bars you bought.
• 🏃‍♀️Consistent Speed: If you run at a constant speed (r) for 3 hours and travel 15 miles, then $3r = 15$, where r is your speed.

💡 Tips and Tricks

• ✅Always Check Your Answer: Substitute your solution back into the original equation to make sure it's correct.
• ✍️Show Your Work: Writing out each step can help prevent mistakes.
• ➕Remember the Sign: Pay close attention to positive and negative signs, especially if 'a' or 'b' are negative numbers.

📝 Practice Quiz

Solve the following equations:

1. $5x = 25$
2. $2x = 14$
3. $4x = 32$
4. $6x = 42$
5. $7x = 49$
6. $8x = 64$
7. $9x = 81$

Answers:

1. $x = 5$
2. $x = 7$
3. $x = 8$
4. $x = 7$
5. $x = 7$
6. $x = 8$
7. $x = 9$

✅ Conclusion

Solving one-step multiplication equations is a fundamental skill in algebra. By understanding the principle of inverse operations and following a step-by-step approach, you can confidently tackle these equations. Keep practicing, and you'll become a pro in no time!