\[ 7(2q + 8) + 15q = 105 \] - Coaching Toolbox
Solving 7(2q + 8) + 15q = 105: Step-by-Step Guide
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
Image Gallery
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:
📰 cast of movie atomic blonde 📰 actors on rizzoli & isles 📰 searching for bobby fischer 📰 Vygotsky Proximal Zone 8364667 📰 Nrp Stock Is Crashingbut Early Investors Are Hitting The Jackpotdiscover Why 165208 📰 Can Johnny Homicidal Walk Free Unbelievable Details You Wont Believe 3001200 📰 The Ultimate Guide To Perfect Azure Naming Conventions That Save Time Money 4589836 📰 Petecut Just Launched Something Shockingthis Pet Industry Game Changer Will Blow Your Mind 4466657 📰 Revamp Your Photo Management Todaydiscover Microsoft Office Picture Managers Top Tips Now 3502940 📰 This Flippity Trick Will Leave Your Friends Screaming For More 7616893 📰 Prime Definition Psychology 1247168 📰 Golden Retriever Puppy 3415918 📰 Secret Storage Secrets To Transform Your Messy Living Room Into A Display Of Style 7574542 📰 Spartanburg Methodist College 8103186 📰 Barrel That Rolls Like A Rockyou Wont Believe What Actually Happens Next 4410194 📰 Great Cooling Fans 517648 📰 Standard Nuclear The Shocking Truth Behind Its Life Saving Power 4976057 📰 How Krypto The Superdog Became The Face Of Crypto Gaming Investment 1372065Final 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)
