Solve: −9 < 2x − 5 < 9 → −4 < 2x < 14 → −2 < x < 7. - ECD Germany
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.
Image Gallery
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:
📰 A cartographer digitizes historical maps using a scanner that processes 4.8 pages per minute. If a collection of 72 maps, each 15 pages long, is scanned continuously, how many hours are required to complete the project? 📰 An entomologist studies pollination efficiency: each butterfly visits 22 flowers per hour and transfers pollen to 85% of them successfully. If a field needs 1,320 successful pollinations, how many hours must 6 butterflies work collectively? 📰 USD and SEK Collision: This Surprising Trade Could Impact Your Forex Portfolio Instantly! 📰 Where To Stream 8574415 📰 Pocket Monsters Roblox 6643287 📰 Surprisingly Easy Beef Ribs In Oven That Will Mesmerize Your Taste Buds 7905029 📰 Presence 2024 The Mind Blowing Sci Fi Film You Wont Be Able To Ignore 5362293 📰 Jagx Stock Soared Over 500Heres Why Investors Are Eating It Up In 2024 5685617 📰 Get The Ultimate Long Wolf Cutyour New Favorite Hairstyle That Wows Everyone 6497874 📰 Iad Weather 8411756 📰 Appheaven Is Hidden Behind These Simple Tricksyou Need To See This 3656893 📰 Kissh Revealed The Secret That Will Make You Forget Everything You Know 1853789 📰 Doja Cat Joseph Quinn 5188888 📰 Sandyhook 1266623 📰 Discover Secret Tricks To Npi Search By Nameunlock Your Names Hidden Details Fast 8267453 📰 J Outsourcing Production To Reduce Overhead Costs 1126723 📰 Taqueria Garibaldi 6060579 📰 Ice Raids Boston 7812228Final 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:
$$
-2 < x < 7
$$
