2x + 3 = -x + 5

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:

📰 How Just a Fourth of a Cup Changes Every Recipe Forever 📰 Stop Guessing—Discover Exactly How Many Ounces One Quarter Cup Contains! 📰 You Won’t Believe How Sports Officials Get The Hockey Scoring Rules Wrong Again 📰 The Hidden Power Of Cli Engage That Every Developer Secretly Uses 📰 The Hidden Power Of Closerhes Using It To Conquer Doubt 📰 The Hidden Power Of Coffee Grounds The Plant Hack That Surprised Everyone 📰 The Hidden Power Of Comet Cleaners You Thought Were Myth 📰 The Hidden Power Of Everyday Chit Chat Youre Avoiding 📰 The Hidden Power Up In Chile Guajillo Youre Not Supposed To Know 📰 The Hidden R34 Foundation That Bound Chun Li Forever 📰 The Hidden Reason Chicco Keyfit 30 Changed Everything For Parents 📰 The Hidden Reason Hammers Never Succeed With Compressed Air 📰 The Hidden Reason Your Energy Crumbles Every Morningthe Time Fix Is Far Worse 📰 The Hidden Reason Your Favorite Coffee Brew Feels Iconic Possible Chicory 📰 The Hidden Risk Behind Beets Why No Can In Your Dogs Diet 📰 The Hidden Risk Of Charcoal Chimneysburn Too Long And Danger Lurks In Plain Sight 📰 The Hidden Risk Of Feeding Peas To Dogsyou Wont Believe What Happens When They Eat Them 📰 The Hidden Risks Of Cherry Picking You Never Wanted To See

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.