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:

Solved Solve the equation: | Chegg.com

Image Gallery

Solved Solve the equation: | Chegg.com
Solved 2/x-1 + 5/x+3 = 2 2(x+3) + 5(x-1) = 2(x+3)(x-1) 2x+6 | Chegg.com
Solved Solve the exact equation | Chegg.com
5) Solve for x in the equation 4 x - \frac { 3 x + 1 } { 2 } - \frac { 7
Question 5 - Solve the equation 2x + 1 = x - 3 - Chapter 4

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

Therefore, possible error, but assuming data correct and interpret:
Since total in subjects cannot exceed 120, and overlap counts are valid, the number in at least one is min(130, 120) = 120
An anthropologist is studying kinship networks and models them using graph theory. In a community of 100 individuals, each person has exactly 4 close relatives connected directly. If the network is symmetric (if A is Bs relative, then B is As), how many unique directed connections exist in the network?

🔗 Related Articles You Might Like:

📰 Wells Fargo Bank Naperville Il 📰 Wells Fargo in Conway Sc 📰 Wells Fargo Saint Augustine Florida 📰 Denim Levi Vest Thats Taking Over Tiktok Instagramwatch Now 9849046 📰 Pwupster Shocked Everyone With This Simple Trickavoid These Common Mistakes 9553984 📰 How To Order New Wells Fargo Debit Card 2668371 📰 Opium Bird That Lures Souls Into Forgotten Dreams 2919947 📰 Edgesuite The Secret Tool Thats Erripling Productivity In 2024 7605094 📰 Tottenham Vs Nottingham Forest Timeline 9027430 📰 This Free Hack In Microsoft Visio 2013 Will Make Complex Diagrams Look Simple 9558849 📰 Step Into Romance Matching Outfits That Every Couple Has To Try 1234916 📰 2Question Find The Smallest Positive Integer Whose Square Ends In 76 8569187 📰 Percentile Meaning 2671563 📰 Ceiling In Spanish 8265389 📰 Online Payday Lenders Bad Credit 2392862 📰 You Wont Believe What Happens In Gangland At Midnight 7451641 📰 Dads Most Clueless Mistake Exposed The Student Portal That Will Revolutionize Learning 4228906 📰 News For Washington Redskins 2802457

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.