Finding the Value of x in Linear Equations is Easy!

Cracking Linear Equations: A Simple Guide to Variables

You ever look at a math problem and think, "Yeah, this seems tricky but I can handle it!"? Well, if you're gearing up for the Ontario Mathematics Proficiency Test, you're not alone! Let's tackle one of the simplest yet fundamental concepts in algebra: solving for a variable.

The Equation Breakdown: What’s the Problem?

Take a look at this equation:

[ x + 4 = 15 ]

Looks familiar, right? In this equation, we want to find out what value of ( x ) makes the statement true. This little process of unraveling what ( x ) actually is? That’s your goal!

Step 1: Isolate the Variable

First off, we need to isolate ( x ). It’s like finding that secret ingredient in a recipe. To do this, we follow a simple rule: whatever you do to one side of the equation, you must do to the other side!

So, our first step will be to get rid of that pesky +4. We can do this by subtracting 4 from both sides:

[ x + 4 - 4 = 15 - 4
]

This simplifies to:

[ x = 15 - 4 ]
[ x = 11 ]

And voila! Just like that, we’ve found that ( x ) is 11! Not so scary, huh?

Why Does This Work?

You might wonder, "How did we know to subtract 4?" Well, that’s the beauty of algebra! Each part of the equation is a balance. We’re just making sure both sides remain equal while we get to the heart of ( x ).

Checking Our Work

Let’s not stop here! A good practice is to always check your work. So if we substitute 11 back into the equation to double-check:

[ 11 + 4 = 15 ]

Isn’t that satisfying? It holds true! When we add 4 to 11, we get 15, confirming our solution.

What About the Other Choices?

Just for clarity, let's look at why the other options don't work.

• If ( x = 7 ): ( 7 + 4 = 11 ) (not equal to 15)
• If ( x = 15 ): ( 15 + 4 = 19 ) (not equal to 15)
• If ( x = 19 ): ( 19 + 4 = 23 ) (not equal to 15)

So only ( x = 11 ) is the real deal.

Bringing it All Together

Solving for variables like this is a key concept in mathematics. Whether you’re working through practice problems or gearing up for your exams, knowing how to isolate a variable is crucial! It's all about understanding how to manipulate the equation to get to your answer.

So, the next time you face a linear equation, remember this method! When you isolate that variable, you're not just solving; you're building confidence!

And there you have it! Whether you’re in the classroom or working through exercises at home, solving equations is your ticket to mastering math. Keep practicing, and you’ll be ready to rock your math test! 🌟