Mastering the Equation: How to Solve for X with Ease

Find the value of x in the equation x/3 + 2 = 5.

• A. x = 9
• B. x = 12
• C. x = 15
• D. x = 6

Answer: (A)

To find the value of \( x \) in the equation \( \frac{x}{3} + 2 = 5 \), we can follow these steps: 1. Start by isolating the term with \( x \). First, subtract 2 from both sides of the equation to simplify it: \[ \frac{x}{3} = 5 - 2 \] This simplifies to: \[ \frac{x}{3} = 3 \] 2. Next, to eliminate the fraction, multiply both sides of the equation by 3: \[ x = 3 \times 3 \] This results in: \[ x = 9 \] This shows that the solution \( x = 9 \) is correct because, when substituted back into the original equation, it satisfies the condition. If you were to substitute \( x = 9 \) into \( \frac{x}{3} + 2 \), you would get: \[ \frac{9}{3} + 2 = 3 + 2 = 5 \] Thus proving that the left-hand side equals the right-hand side,

When faced with an equation like ( \frac{x}{3} + 2 = 5 ), your first thought might be, "How do I even start?" Don’t worry, that’s a common feeling! Solving for ( x ) isn’t just a task to get through; it’s a skill that can be developed with practice and a little know-how. So, let’s break this down together!

You might wonder why isolating ( x ) feels like finding a needle in a haystack sometimes. But, trust me, it gets easier with each problem you tackle. Here, we’ll isolate ( x ) step by step so you can say goodbye to confusion and hello to clarity!

Step 1: Simplify the Equation

First, let’s tackle the equation head-on. Our equation is initially set up as:

[

\frac{x}{3} + 2 = 5

]

The goal is to isolate that pesky ( x ). Here’s the thing—subtracting 2 from both sides helps simplify things down to this:

[

\frac{x}{3} = 5 - 2

]

This simplifies into:

[

\frac{x}{3} = 3

]

Already feeling a bit clearer about what we're looking for? Great!

Step 2: Get Rid of the Fraction

Now, to free ( x ) from its fraction cage, we multiply both sides by 3. This step is key to unlocking the full potential of your equation. Here’s how it looks:

[

x = 3 \times 3

]

And just like that, we find:

[

x = 9

]

Verifying the Solution

At this point, it's always good to double-check your work. After all, nobody likes to get burned on a simple mistake! Substitute ( x = 9 ) back into the original equation:

[

\frac{9}{3} + 2

]

This equates to:

[

3 + 2 = 5

]

It checks out, left side equals right side—boom! You’ve just proven your solution!

Conclusion

Being able to solve for ( x ) is like a rite of passage in the world of math. It sets the stage for more complex concepts down the line, opening up new doors to understanding algebra and beyond. So, if math isn’t your favorite subject, don’t throw in the towel just yet. Embrace these equations like puzzles to solve!

Having strategies in place makes studying for the Mathematics ACT Aspire Test feel a little less daunting. Wouldn’t it be nice if every math problem felt this way? With practice, they can! So go ahead and embrace the challenge; understanding these little victories lays the foundation for much bigger successes in math and life!