Unlock The Mystery: Solve X 4 5x 2 9 Now!

In the world of algebraic equations, it's not uncommon to come across puzzles that intrigue and challenge both students and seasoned mathematicians. One such equation is X + 4 - 5X + 2 = 9. Today, we'll delve deep into this equation, understanding its structure, breaking it down into manageable steps, and solving it together.

Understanding the Equation

Before we dive into the actual solving process, let's clarify the equation:

• X represents the variable we need to find.
• 4 and 2 are constants on the right side of the equation.
• -5X is a term involving the variable X, where X is multiplied by -5.

Breaking it Down

The given equation:

X + 4 - 5X + 2 = 9

Here's how we can break it down:

1. Combine like terms: The X and -5X are like terms because they both contain X.
2. Isolate the variable: Group all X terms on one side and constants on the other.
3. Solve for X: Once isolated, perform operations to find X.

Step-by-Step Solution

Step 1: Combine like terms

X - 5X + 4 + 2 = 9

Combine X and -5X:

X - 5X = -4X

So, now our equation is:

-4X + 4 + 2 = 9

Step 2: Combine constants

Add 4 and 2:

-4X + 6 = 9

Step 3: Isolate the variable

Move constants to one side to isolate X:

-4X = 9 - 6

Which simplifies to:

-4X = 3

Step 4: Solve for X

Divide both sides by -4:

X = 3 / -4

So, X = -0.75.

Practical Examples

Let's look at some scenarios where this equation could come up:

• Physics: Imagine an object moving in two directions with different velocities, where X is the time taken to reach the object's initial position.
• Economics: If X represents the price decrease or increase needed to balance supply and demand in a market.

Shortcuts

For quick calculations:

• Simplification: Notice how X terms combine to make calculations easier.
• Substitution: You can use the equation's structure to quickly test potential answers.

<p class="pro-note">⚡ Pro Tip: Remember, when combining like terms, watch for the signs to ensure correct arithmetic operations.</p>

Advanced Techniques

Factoring

Although not necessary here, factoring can be a powerful tool in solving more complex equations.

Cross-Checking

After solving:

• Substitute X = -0.75 back into the original equation to verify.

Here's the equation with the result:

-0.75 + 4 - 5 * (-0.75) + 2 = 9

-0.75 + 4 + 3.75 + 2 = 9

9 = 9, confirming our solution is correct.

Common Mistakes to Avoid

• Forgetting the negative sign: Not considering the sign of the -5X.
• Misplacing terms: Ensure you're placing terms on the correct side during isolation.

Troubleshooting

If your equation isn't balancing:

• Check your sign work: Correct sign manipulation is crucial.
• Recheck term combination: Ensure all like terms have been correctly combined.

Wrapping Up

Through this exploration of X + 4 - 5X + 2 = 9, we've navigated through the steps of simplification, solving, and verification. Here's what we've learned:

• Equation structure: Recognizing and grouping like terms simplifies the solving process.
• Isolation: Isolating the variable is key to finding its value.
• Verification: Always check your solution in the original equation.

Be sure to keep practicing and explore related algebraic tutorials to hone your skills. Don't forget to test different scenarios to deepen your understanding of how equations like this apply to real-world problems.

<p class="pro-note">📝 Pro Tip: Practice with different equations to understand the nuances of algebraic manipulation.</p>

<div class="faq-section"> <div class="faq-container"> <div class="faq-item"> <div class="faq-question"> <h3>Can I use different methods to solve this equation?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Yes, although we covered one method here, alternative methods like graphical methods or substitution can also be used to solve algebraic equations.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>What if the equation had more terms or variables?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>You would still follow the same steps of combining like terms, isolating variables, and solving. However, the complexity would increase, and you might need more advanced techniques or system solving methods.</p> </div> </div> <div class="faq-item"> <div class="faq-question"> <h3>How can I check my work in more complex equations?</h3> <span class="faq-toggle">+</span> </div> <div class="faq-answer"> <p>Use the same technique of substituting your answer back into the equation. If the left-hand side equals the right-hand side, your solution is correct.</p> </div> </div> </div> </div>