Solve: −9 < 2x − 5 < 9 → −4 < 2x < 14 → −2 < x < 7. - IQnection
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:
📰 ight)^2 - 12\left( rac{3}{2} 📰 ight) + 9 = 4 \cdot rac{9}{4} - 18 + 9 = 9 - 18 + 9 = 0 📰 Thus, the minimum heat loss is 0 units at \( t = rac{3}{2} \) hours. 📰 It Works Like A Pro The Ring App For Iphone That Saves You Paindownload Today 8974451 📰 Vlc Media Player For Mac 194614 📰 Governor Newsom Press Office 5258191 📰 Voov Stock Alert Crashing To 1 Timing This Move Could Beat The Market 411928 📰 Claude Ai Chat 4336228 📰 Sub For Sour Cream 1309581 📰 Why Everyones Obsessed With This Cute Yet Quiet Timid Nature Pokmon 3146107 📰 What Does Pregnancy Discharge Look Like 3219235 📰 Stop Tolerating Mould Heres The Shocking Vinegar Trick That Actually Works 6272215 📰 Mx Bikes Steam 7154445 📰 Casting The Wolf Of Wall Street 7226870 📰 Fifa Peace Prize Trump 8520888 📰 The Name You See Could Change Everythingclaims Epsteins Deepest Allegiances Exposed 6154673 📰 Dailymotion Download 7295511 📰 Upro Etf Shocking Gains That Will Make You Rethink Your Investment Strategy 4358014Final 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:
$$
-2 < x < 7
$$
