Solve: −9 < 2x − 5 < 9 → −4 < 2x < 14 → −2 < x < 7. - High Altitude Science
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:
📰 The Surprising Star Sign for October 26: Astrology Reveals Your Hidden Potential! 📰 October 26 Stargazers: This Exact Star Sign Unlocks Your Cosmic Destiny! 📰 Revealed! Your Perfect Star Sign for October 26 — Match Your Fate Today! 📰 Starve A Fever Feed A Cold 📰 Starved Rock Cabins 📰 Starving Games Cast 📰 Starving Games 📰 Staryu 📰 State Fair Corn Dogs 📰 State Fish Of Hawaii 📰 State Of Decay 3 Release Date 📰 State Of Emergency Game 📰 State Of Play 2025 📰 Statement Earrings 📰 Statement Necklaces 📰 Statesman 📰 Static Shock Animated 📰 Static ShockFinal 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:
$$
-2 < x < 7
$$
