Solve: −9 < 2x − 5 < 9 → −4 < 2x < 14 → −2 < x < 7. - Tacotoon
Solving the Inequality −9 < 2x − 5 < 9: A Step-by-Step Guide
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.
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:
🔗 Related Articles You Might Like:
📰 Can Sonic’s World Embrace an Invisible Force So Powerful It’s Destroying Reality? 📰 Sonic’s Hidden Inflation Crisis: The Twist No One Saw Coming 📰 What Innocent Speed Swipe Unleashed a Floood of Sonic-Fueled Inflation? 📰 Is This The Ultimate Guide To Tetu Dizain Life Changing Design Hacks Inside 📰 Is This The Ultimate Invincible Tech Jacket Youve Been Waiting For Find Out Now 📰 Is This The Ultimate List Of Switch 2 Gamecube Games Every Nostalgia Fan Overseeks 📰 Is This The Ultimate Stormfly Its Locked Tighter Than A Hurricane Finds Out 📰 Is This The Ultimate Street Fighter Alpha 3 Power Insane Alpha Fight Secrets Inside 📰 Is This The Ultimate Switch 2 Emulator Find Out In This Shocking Review 📰 Is This The Ultimate Switch Clone That Steals Your Game Time 📰 Is This The Ultimate Tarn Transformers Muscle Move Watch Now 📰 Is This The Ultimate Upgrade Super Mario 3D World Super Mario Drops Hidden Masterpieces 📰 Is This The Ultimate Upgrade Tecan 3 Breaks All Records In Precision Science 📰 Is This Why Millions Are Talking About Tanya Degurechaff Her Secrets Shocked Everyone 📰 Is Today The Day Expert Reveals The Sweeping Switch Release Date Now 📰 Is Trust Building Too Much See How Bed Tanning Delivers Instant Radiance 📰 Is Your 2025 Aligned Discover The Tamil Calendar 2025 Secrets Now 📰 Is Your Body Reacting Already This System Shock Game Secrets Will Shock YouFinal 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:
$$
-2 < x < 7
$$
