📚 What are One-Step Equations?
A one-step equation is a simple math problem that can be solved in just one step! It involves a variable (usually represented by a letter like $x$ or $y$) and requires you to isolate that variable to find its value. Think of it like solving a mini-mystery! 🕵️♀️
📜 A Little History
While simple equations have likely been around for ages, the use of symbolic algebra, including variables like $x$ and $y$, really took off in the 16th and 17th centuries. Mathematicians like François Viète helped standardize the notation we use today, making it easier to express and solve these equations. 🤓
➗ Key Principles of One-Step Equations
- ➕Addition Principle: ➕ If you're subtracting a number from the variable, add that number to both sides of the equation to isolate the variable.
- ➖Subtraction Principle: ➖ If you're adding a number to the variable, subtract that number from both sides of the equation.
- ✖️Multiplication Principle: ✖️ If the variable is being divided by a number, multiply both sides of the equation by that number.
- ➗Division Principle: ➗ If the variable is being multiplied by a number, divide both sides of the equation by that number.
- ⚖️The Golden Rule: ⚖️ Whatever you do to one side of the equation, you MUST do to the other side to keep it balanced!
📝 Examples to Make it Clear
Let's look at some examples:
- Example 1: Addition: $x - 5 = 12$
To solve for $x$, add 5 to both sides:
$x - 5 + 5 = 12 + 5$
$x = 17$
- Example 2: Subtraction: $y + 8 = 20$
To solve for $y$, subtract 8 from both sides:
$y + 8 - 8 = 20 - 8$
$y = 12$
- Example 3: Multiplication: $\frac{z}{3} = 6$
To solve for $z$, multiply both sides by 3:
$\frac{z}{3} * 3 = 6 * 3$
$z = 18$
- Example 4: Division: $4a = 24$
To solve for $a$, divide both sides by 4:
$\frac{4a}{4} = \frac{24}{4}$
$a = 6$
🌍 One-Step Equations in Real Life
- 🍕Sharing Pizza: 🍕 If you and three friends want to share a pizza equally, and the pizza has $x$ slices, the equation is $\frac{x}{4} = ext{number of slices each}$. If each person gets 3 slices, then $\frac{x}{4} = 3$. Multiplying both sides by 4 gives $x = 12$ slices in the pizza.
- 🛍️Buying Candy: 🛍️ You have $x$ dollars and spend $5 on candy. You now have $7 left. The equation is $x - 5 = 7$. Adding 5 to both sides gives $x = 12$ dollars.
- 🏃Running Laps: 🏃 You run $x$ laps around a track. If one lap is 400 meters and you run 2000 meters total, the equation is $400x = 2000$. Dividing both sides by 400 gives $x = 5$ laps.
💡 Conclusion
One-step equations are the building blocks for more complex math problems. By understanding the basic principles and practicing regularly, you'll become a pro at solving them! Keep practicing and don't be afraid to ask for help! 👍
