Solve: −9 < 2x − 5 < 9 → −4 < 2x < 14 → −2 < x < 7. - NBX Soluciones
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:
📰 Shocking Hack to Download Windows 11 22H2—Your System Upgrade Starts Now! 📰 Top 10 Perfectly Compatible Windows 11 CPUs That Power Your PC Like a Pro! 📰 You Wont Believe Which CPUs Actually Work WITH Windows 11 Instantly! 📰 Unbelievable Secrets Hidden Inside This Aat Store 7320079 📰 Student Power Move Grab Microsoft Office At Top Student Prices Today 3707002 📰 Connections Hint July 20 9792310 📰 Trump Banning Gender Affirming Care 240183 📰 Green Cove Springs Secrets Revealed You Wont Believe What Lies Beneath The Waters 875704 📰 What Is A Bond Fund 4623246 📰 Base Near Forbidden Games Premium Access Now Live 2482293 📰 Powerball Numbers For September 1 1213774 📰 Peppermint Ice Cream 6789510 📰 Cast Mike Molly 2546234 📰 Kate Upton Tits 1044145 📰 However For Consistency With Format And Since Other Answers Are Integers Perhaps The Number Refers To Total Success Events But The Question Says Flowers 8541039 📰 What Harry Potter On Did The World Think It Could Never Bespoilers Inside 4680540 📰 Iphone Screens Anew The Ultimate Collection Of Dirty Emojis Hidden From Plain View 6027167 📰 Canelo Vs Crawford Results 9320062Final 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:
$$
-2 < x < 7
$$
