Solving 7(2q + 8) + 15q = 105: Step-by-Step Guide

Understanding how to solve equations like 7(2q + 8) + 15q = 105 is essential for mastering algebra. Whether you're a student learning basic linear equations or looking to sharpen your problem-solving skills, this step-by-step breakdown will help you confidently solve for q.

What is the Equation?

Understanding the Context

We start with the equation:
7(2q + 8) + 15q = 105

This equation contains parentheses, variables on both sides, and constants. We’ll simplify and isolate q using fundamental algebraic operations.


Step 1: Expand the Parentheses

Key Insights

Apply the distributive property to expand 7(2q + 8):
7 × 2q = 14q
7 × 8 = 56

So:
14q + 56 + 15q = 105


Step 2: Combine Like Terms

Combine the q terms:
14q + 15q = 29q

🔗 Related Articles You Might Like:

📰 You Won’t Believe This Hidden Gem for Sale! 📰 Leopard Gecko for Sale—Frilled Pattern & Perfect Stripes! 📰 Take A Sip And Never Look Back! The Shocking Truth About Leche Evaporada 📰 This Grey Jordans Story Will Change How You View Sneaker Culture Forever 📰 This Grey Skirt Look Will Turn Every Outfit Into A Fashion Statementyou Wont Believe How Stylish It Is 📰 This Grey Suit Suit Is Taking Fashion By Stormyou Wont Believe How Sleek It Looks 📰 This Griddy Dance Trend Shook The Charts See The Choreography Everyones Copying 📰 This Grievous Grievous Case Is Going Virallearn How Its Changing Public Opinion Now 📰 This Griffins Star Just Revealed The Peter Behind His Griffin Identity Genius Or Ridiculous 📰 This Grill By Granted One Miracle Recipe Watch Your Dishes Go Viral 📰 This Grilled Ribeye Will Blow Your Mind You Wont Believe How Juicy It Is 📰 This Grilled Shrimp Marinade Armies 10 Flavors Youll Never Eat Plain Shrimp Again 📰 This Grimm Fantasy Game Now Dominates Mystery Gamesheres Why 📰 This Grimm Series Twist Proved The Series Is Darker Than Ever Watch The Full Story 📰 This Grinch Onesie Is So Cute Itll Make You Snort Your Coffee Away Dont Miss It 📰 This Grinch Punch Goes Viralwitness The Night Holiday Spirit Died 📰 This Grinch Shirt Is Taking Over Social Media You Need One Ton Before Christmas 📰 This Grinch Wallpaper Is A Game Changerdownload Now Before The Festive Season Spoils Everything

Final Thoughts

Now the equation is:
29q + 56 = 105


Step 3: Isolate the Variable Term

Subtract 56 from both sides to isolate the term with q:
29q + 56 - 56 = 105 - 56
29q = 49


Step 4: Solve for q

Divide both sides by 29:
q = 49 ÷ 29
q = 49/29


Final Answer

q = 49/29
or approximately q ≈ 1.69 (when rounded to two decimal places)