Unlocking Algebra: Your Guide to Solving Equations with Variables

Ever feel like algebra is a secret code you're desperate to crack? Don't worry, you're not alone! Let's demystify those equations and unlock the power of solving for variables.

What Exactly is an Equation?

Think of an equation like a balanced scale. Both sides need to be equal. You've probably seen simple equations like this:

• 2 + 3 = 5

This tells us that 2 plus 3 equals 5, which we already know! But things get more interesting when we introduce variables.

Variables: The Mystery Guests

A variable is like a placeholder, represented by a letter (like 'x' or 'y'). It stands for a number we don't know yet.

Let's look at an example:

• 7x = 14

This equation tells us that 7 times some unknown number ('x') equals 14. Our mission? To find out what 'x' is!

Solving for 'x': Becoming an Equation Detective

Here's where the fun begins! To solve for 'x', we need to isolate it on one side of the equation. Think of it like this: we want 'x' all by itself, like the star of the show!

How do we do that? By using the opposite operation:

• The equation says: 7 times x = 14
• We need to do the opposite: 7 divided by 7 = 1 (which leaves 'x' by itself!)

Remember the Golden Rule: Whatever we do to one side of the equation, we must do to the other side to keep things balanced.

So, let's divide both sides of the equation by 7:

• (7x) / 7 = 14 / 7

This simplifies to:

• x = 2

We did it! We solved for 'x'! We now know that 'x' equals 2.

Let's Practice!

Ready to test your new detective skills? Try solving this equation:

• 3y + 5 = 14

Here's how to approach it:

1. Isolate the variable term: Subtract 5 from both sides of the equation.
2. Isolate the variable: Divide both sides of the equation by 3.

Solution:

1. 3y + 5 - 5 = 14 - 5 (This simplifies to 3y = 9)
2. (3y) / 3 = 9 / 3 (This simplifies to y = 3)

You did it again! You found out that 'y' equals 3.

Keep in Mind:

• Always keep the equation balanced by performing the same operation on both sides.
• Use the opposite operation to isolate the variable.
• Don't be afraid to practice! The more you practice, the more confident you'll become.

Algebra might seem like a puzzle at first, but with a little practice, you'll be solving equations like a pro in no time!

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