Solving Linear Equations: Step-by-Step Guide to Solve for $ x $

Finding the value of $ x $ in a linear equation is a fundamental skill in algebra that helps build problem-solving confidence. One common equation students encounter is:

$$
4(x - 3) + 2 = 2(2x + 1) - 6
$$

Understanding the Context

In this article, we’ll walk through how to solve this equation step by step, making it clear how simplifying both sides and isolating $ x $ leads to the correct solution.

Step 1: Expand Both Sides

Start by applying the distributive property to both sides of the equation:

Question: Solve for $ x $ in the equation $ 4(x - 3) + 2 = 2(2x + 1) - 6 $

Key Insights

$$
4(x - 3) + 2 = 2(2x + 1) - 6
$$
$$
4x - 12 + 2 = 4x + 2 - 6
$$

Now simplify both sides:

Left side:
$$
4x - 10
$$
Right side:
$$
4x - 4
$$

So the equation becomes:
$$
4x - 10 = 4x - 4
$$

Continue Reading

The Secret Law Firm Behind Every Major Court Victory
You’ve Been Using CNLAWBLOG Without Realizing This Hidden Power
How Cnlawblog Exposed the Real Rules No One Talks About

🔗 Related Articles You Might Like:

📰 Therefore, the number of distinct sequences is $ \boxed{1260} $.Question: A technology consultant models data flow efficiency using the function $ f(\theta) = \sin^4 \theta - 4\sin^2 \theta \cos^2 \theta + \cos^4 \theta $. Find the minimum value of $ f(\theta) $ over all real $ \theta $. 📰 Solution: We begin by rewriting $ f(\theta) $ using trigonometric identities. Observe: 📰 f(\theta) = \sin^4 \theta - 4\sin^2 \theta \cos^2 \theta + \cos^4 \theta. 📰 Two Face Two Face 📰 Two Face Villain Batman 📰 Two Face 📰 Two Faced Harvey Dent 📰 Two French Braids 📰 Two Letter Words 📰 Two Men Kissing 📰 Two Men Sitting On A Couch 📰 Two Of Cups 📰 Two Of Wands 📰 Two People Yoga Poses 📰 Two Piece Set 📰 Two Piece Skirt Set 📰 Two Piece 📰 Two Player Card Games

Final Thoughts

Step 2: Eliminate Common Terms

Notice that $ 4x $ appears on both sides. Subtract $ 4x $ from both sides to eliminate the variable term temporarily:

$$
4x - 10 - 4x = 4x - 4 - 4x
$$
$$
-10 = -4
$$

Step 3: Analyze the Result

We now have the false statement:
$$
-10 = -4
$$

This is not true, meaning there is no solution to the original equation.

What Does This Mean?

When simplifying both sides leads to a contradiction like $-10 = -4$, it indicates that the equation has no solution—it’s inconsistent. In other words, no value of $ x $ satisfies the original equation.