2x + 3 = -x + 5 - Get link 4share

Understanding and Solving the Equation: 2x + 3 = -x + 5

Solving linear equations is a fundamental skill in algebra, essential for students, educators, and professionals alike. One commonly encountered equation is 2x + 3 = -x + 5, which may seem simple at first glance but offers a great opportunity to reinforce algebraic thinking.

Understanding the Context

What Is the Equation 2x + 3 = -x + 5?

The equation 2x + 3 = -x + 5 sets two expressions equal to each other: on the left, 2 times a variable x plus 3; on the right, negative x plus 5. Solving this equation means finding the value of x that makes both sides equal. This process strengthens problem-solving and critical thinking skills.

Step-by-Step Solution

Key Insights

Step 1: Eliminate the variable on one side
Start by moving all x terms to one side (here, the left) and constant terms to the other side (here, the right):

2x + 3 = -x + 5 2x + x + 3 = 5

2x + x = 3x, so the equation becomes:

3x + 3 = 5

Step 2: Isolate the x term
Subtract 3 from both sides to isolate the term with x:

🔗 Related Articles You Might Like:

📰 Las Palmas Surprises Barcelona in Las Palmas Derby—T Botanian Miracle Threatens Champions 📰 From Underdogs to Thunder—U. D. Las Palmas Explode on Barcelona in Historic Clash 📰 How Las Palmas Drove Barcelona from Its Seat in a Match for the Ages 📰 The Miracle Ingredient Many Ignorehow Orchid Bark Secretly Transforms Your Plants 📰 The Miracle Name In Mcdouble Is Twisting Your Healthand You Didnt See It 📰 The Miracle Of San Miguel Arcangel Will Change Your Life Forever 📰 The Miracle Under Your Feet That Nature Hides From You 📰 The Mischievous Too S Winey Monkey Jellycat That Baffles Entire Jungles 📰 The Misinformation About Mugwort Tea Will Shock Youherbs Dont Always Deliver What They Promise 📰 The Missing O2 Lewis Structure Everyone Swears Is Key To Mastering Bonds 📰 The Missing P0430 Code That Will Explode Your Mind 📰 The Missing Piece Owlexpress Was Using To Dominate The Market 📰 The Mistaken Mustard Seed That Can Transform Your Life Beyond Expectations 📰 The Moment A Motorcycle Went Down Turned A Local Epidemic Into Silent Tragedy 📰 The Moment His 25 Liter Nachro Vidal Shocked The Worldthis Expensive Perfume Bottle Speaks Volumes 📰 The Moment His Spirit Fadedwhat Really Happened To That Unseeing Smile 📰 The Moment I Held It My Dreams Changed Forever 📰 The Moment I Realized Who My Real Friends Really Are

Final Thoughts

3x + 3 - 3 = 5 - 3 3x = 2

Step 3: Solve for x
Divide both sides by 3:

x = 2 ÷ 3 x = $\frac{2}{3}$

Verifying the Solution

Substitute $x = rac{2}{3}$ back into the original equation:

Left side:
2x + 3 = 2($\frac{2}{3}$) + 3 = $\frac{4}{3}$ + 3 = $\frac{4}{3}$ + $\frac{9}{3}$ = $\frac{13}{3}$

Right side:
-x + 5 = -\frac{2}{3} + 5 = -\frac{2}{3} + \frac{15}{3}$ = $\frac{13}{3}$

Both sides equal $rac{13}{3}$, confirming the solution is correct.