How to Solve the Equation 3(x - 1) + 4 = 10: A Simple Guide

Unlocking the Mystery: Solving 3(x - 1) + 4 = 10

When faced with equations like 3(x - 1) + 4 = 10, it might seem daunting at first—it’s almost like staring at a puzzle waiting to be solved! But fear not! We’re going to break this down step by step. You know what they say, the first step is always the hardest, right?

Let’s Get Started!

The beauty of solving equations lies in the simplicity that emerges once you dive in. Here’s the first step:

1. Distributing the 3: Look closely at 3(x - 1). It’s like a small package that we need to unwrap. Just like opening a gift, we distribute the 3 to both terms inside the parentheses:

   [ 3(x - 1) = 3x - 3 ]

   Now, we can substitute it back into our equation:

   [ 3x - 3 + 4 = 10 ]

Combine Forces!

Next up—let’s take a look at the constants. It’s a bit like cleaning up your room; sometimes, things just need to be put together neatly:

• Combine the -3 and 4 on the left side:

  [ 3x + 1 = 10 ]

Isolate that Variable!

Here’s where the fun really begins! We want to get x alone on one side of the equation. It’s like trying to find your favorite book buried under a pile of clothes—it takes a bit of effort. Start by moving that pesky 1:

• Subtract 1 from both sides:

  [ 3x = 10 - 1 ]

  [ 3x = 9 ]

Now, we’ll divide both sides by 3. It’s like sharing a pizza with friends—you cut it up so everyone can have a slice!

[ x = \frac{9}{3} ]

And voilà!
[ x = 3 ]

And There You Have It

So, if you’ve followed along, you’ll see that the value of x is 3. Option B from our choices is correct! Not too bad, right? You can tackle similar problems with practice and confidence.

Tips for the Ontario Mathematics Proficiency Test

As you prepare for the Ontario Mathematics Proficiency Test, remember that mastering the art of solving equations is all about practice. Here’s a tip:

• Work through various problem sets. Problem-solving is like building muscle—you get stronger the more you do it!

Also, don’t hesitate to reach out for help or use resources available to you. Sometimes, having a fresh pair of eyes can make all the difference.

The Final Word

Whether it’s a simple equation or a more complex problem, remember that every mathematical challenge is just an opportunity to learn. So roll up your sleeves and take on those equations one at a time, and you’ll find that math can be as delightful as finding an extra fry at the bottom of your take-out bag. Keep at it!