Solve: −9 < 2x − 5 < 9 → −4 < 2x < 14 → −2 < x < 7. - Sourci
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:
📰 Happy Coffee Bedford 📰 Franz Kafka Metamorphosis 📰 Rpg Definition 📰 What Is National Provider Identification Number 📰 Amc Movies Madison Heights Mi 9052919 📰 Madhouse Coffee 4469626 📰 Shocked By Iacs Stock Price Spikewatch How This Trend Could Double Fast 5663469 📰 Bank Of America In Beaumont Texas 📰 India Vs Bangladesh 1955775 📰 Why Is Gas So Expensive In California 6049699 📰 Charlie Kirk Controversies 6848513 📰 Wxrisk 8085803 📰 Jeffrey Allen 📰 Verizon Chalmette 📰 What Is Compound Growth 📰 Reception Surprise Guests With These Luxury Wine Gifts That Cover Every Occasion 8734182 📰 Bank Of America Getting Euros 📰 Western Digital Software For MacFinal 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:
$$
-2 < x < 7
$$
