2x + 3 = -x + 5 - jntua results

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:

📰 Danny Ketch Exposes the Truth—Guess Who’s Back in the Spotlight?! 💥 📰 Inside Danny Ketch’s Secret Life: The Shocking Truth Everyone’s Talking About! 📰 Danny Rand Iron Fist: The Untold Legend of the Ultimate Dark Knight! 📰 72889 3 17316 C 38 Rightarrow 20223 51948 C 38 Rightarrow C 31725 📰 75 Shocking Secrets Fab Ladies 70S Costumes That Will Fire Up Your Costume Game 📰 7D 1680 Rightarrow D 240 Km 📰 7K 4 Leq 100 Rightarrow 7K Leq 104 Rightarrow K Leq Rac1047 Pprox 14857 📰 8 Places To Find The Best Leather Shorts Easy Shopping Guide Inside 📰 9A 9B 27 Rightarrow A B 3 📰 9A 3B C 18 Quad Textequation 3 📰 A 6 Quad A 3 Quad A Quad A 3 Quad A 6 📰 A 1 📰 A 2Pi 22 2Pi 28 📰 A 2Pi R2 2Pi Rh 📰 A 2Pi Times 4 2Pi Times 16 📰 A 40Pi 📰 A 8Pi 32Pi 📰 A B C 6 Quad Textequation 1

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.