Solving the Inequality −9 < 2x − 5 < 9: A Step-by-Step Guide

Learning how to solve inequalities step-by-step is essential for mastering algebra and building problem-solving skills. One common inequality students encounter is:

$$
-9 < 2x - 5 < 9
$$

Understanding the Context

This compound inequality can seem tricky at first, but breaking it down into smaller, manageable parts makes it easy to solve. In this article, we’ll walk through solving this inequality, explaining each step clearly and showing how to arrive at the final solution:
$$
-2 < x < 7
$$

Understanding the Compound Inequality

The inequality
$$
-9 < 2x - 5 < 9
$$
is a compound inequality involving a expression on both sides. It states that 2x minus 5 lies strictly between –9 and 9. To solve for x, we need to isolate x while maintaining the inequality’s truth.

Solve: −9 < 2x − 5 < 9 → −4 < 2x < 14 → −2 < x < 7.

Key Insights

Step 1: Add 5 to All Parts

To eliminate the constant term –5, add 5 to every part of the inequality:

$$
-9 + 5 < 2x - 5 + 5 < 9 + 5
$$

Simplifying each term:

Continue Reading

Case 2: Both A and B are selected
Then we choose 1 more from the remaining 4:
Total valid selections:

🔗 Related Articles You Might Like:

📰 This Shocking Trick Released the Secret Power of Carbonated Drinks—Drink Up! 📰 Carbonated Drinks: The Hidden Secret Behind Refreshing Refreshment You’ve Always Missed! 📰 Why Carbonated Drinks Are the Ultimate Escape (And Total Nutrition Surprise!) 📰 Shippuden Legends Unveiled The Most Obsessed Naruto Shippuden Characters Explained 📰 Shippuden Uchiha Madara Shock His Dark Past Ready To Shock Every Fan 📰 Shirt That Showcases Muscle Like Never Before Bold Look Inside 📰 Shock Everyone With This Ultra Chic Navy Blue Shirt Thats 2024S Hottest Pick 📰 Shock Everyoneyour Name On This Life Changing Name Plate Necklace Trendsetter 📰 Shock Hacks How Cartoon Networks Network Games Are Taking Over Reality Join The Virtual Revolution 📰 Shock In The Anime World The Shockingly Raw Nato Manga Thats Going Viral 📰 Shock The Internet With These Hyper Detailed Mushroom Clipart Masterpieces 📰 Shock The Real Nba Scoring Titans Breaks Every Record Ever Variing 📰 Shock You The Masterclass Behind The N2 Lewis Structure Revealed 📰 Shock Your Friends With These Perfect Purple Nail Art Designs Shop Now 📰 Shock Your Kids This Simple Multiplication Chart 1 100 Gets Kids Drilling In Seconds 📰 Shocked By Her Power Crime Inside The Rise Of Yoruichi Shihinthis Five Time Betrayal Will Blow Your Mind 📰 Shocked By How Much Space A Murphy Bed Kit Can Savetry It Tonight 📰 Shocked By My Talking Toms Ultimate Personalityplay The Hottest Version Yet

Final Thoughts

$$
-4 < 2x < 14
$$

This step preserves the inequality because we’ve performed the same operation on all three parts.

Step 2: Divide All Parts by 2

Now isolate x by dividing every part of the inequality by 2:

$$
rac{-4}{2} < rac{2x}{2} < rac{14}{2}
$$

Which simplifies to:

$$
-2 < x < 7
$$

Final Result