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

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:

Image Gallery

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

🔗 Related Articles You Might Like:

📰 This Simple Trick Will Unlock 403% More Growth When Rolling Your 401k into an IRA! 📰 Stop Missing Out—Roll Your 401k Into an IRA and Supercharge Your Future! 📰 Unlock Hidden Savings: Rolling Your 401k into an IRA Changes Everything! 📰 Sidney Crosby How Old 5389337 📰 Performance Explosion Awaits Master Business Central Integration Like A Pro 4267405 📰 5 Omg The Lmchart Breakdown Students Experts Are Crazy Aboutdont Miss Out 3518097 📰 Cast Of American Primeval 6271578 📰 From Emperor To Villain Darth Sidious Shocking Rise To Power You Must See 9603356 📰 Detroit Pistons Jersey 8142500 📰 Cheat Table Simpsons Hit And Run Dolphin 4053058 📰 Free Cool Games For Pc 7112178 📰 Sneaker Air Force 1214507 📰 Astroboy 3052116 📰 Microsoft Cloud Pki Secrets Secure Your Data Like A Cyber Pro Overnight 1466056 📰 Hotels Lansing United States 4036756 📰 Download The Firestick Remote App Transform How You Streamclaim Your Free Upgrade 1529802 📰 Holiness Definition 1410090 📰 From Farm To Table The Exquisite Veal Chop That Every Foodie Wants 2021655

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.