\[ 2x + 9x - 15 = 12 \] - Redraw
Solving the Linear Equation: 2x + 9x - 15 = 12 – A Step-by-Step Guide
Solving the Linear Equation: 2x + 9x - 15 = 12 – A Step-by-Step Guide
Solving equations is a fundamental skill in algebra, essential for students, educators, and anyone working in math-intensive fields. One commonly encountered type is the linear equation, such as 2x + 9x – 15 = 12. Whether you're preparing for exams, teaching algebra, or simply brushing up on math fundamentals, understanding how to solve this equation can boost your confidence and problem-solving skills.
This article provides a clear, detailed breakdown of solving 2x + 9x - 15 = 12, including step-by-step instructions, simplification techniques, and practical applications.
Understanding the Context
Understanding the Equation
Start with the equation:
2x + 9x – 15 = 12
This is a linear equation in one variable, x. Linear equations feature variables raised to the first power only, making them relatively straightforward to solve using inverse operations.
Image Gallery
Key Insights
Step 1: Combine Like Terms
The first step in simplifying the equation is combining like terms — specifically, the terms involving x:
2x + 9x = 11x
So the equation becomes:
11x – 15 = 12
🔗 Related Articles You Might Like:
📰 Fidelity Bank Wire 📰 Fidelity Bank Wire Fee 📰 Fidelity Bank Wire Instructions 📰 Define Illustrate 5938415 📰 This Mexican Seafood Feast Will Make Your Taste Buds Do A Backflipshockingly Fresh 986545 📰 Run For Your Wallets The Awards That Made Gaming History In 2024 2868497 📰 Click To Grab Go Tickets Before This Secret Deal Disappears 4886623 📰 Is The Japanese Yen Crashing Market Shock Over New Exchange Rates 8168782 📰 Crapsee Exposed The Shocking Truth Behind This Secret Weapon 2040993 📰 Kitty Macos 266266 📰 Determine The Score Needed In The Fourth Subject 7336294 📰 Comic Planet Revealed The Hidden World Thatll Blow Your Mind 72711 📰 Revealed Godzillas True Heighttaller Than Mount Everest Lets Count 5370414 📰 Kicker Morten Andersen 3443472 📰 Zlow Explained The Shocking Truth Behind This Controversial Trend 4193691 📰 Why Yahoo Finance Is Hype The Explosive Growth Of Wolfspeed You Need To Watch 2761407 📰 This Single Tone Shift Made Her The Hottest Face On Social Media 8293678 📰 A Geographer Analyzing Sea Level Rise Projects That A Coastal Region Will Experience An Average Increase Of 025 Cm Per Month With An Additional 32 Cm Every November Due To Seasonal Storm Activity What Is The Total Projected Rise After 2 Years 170993Final Thoughts
Step 2: Isolate the Variable Term
To solve for x, isolate the term with the variable. Add 15 to both sides of the equation:
11x – 15 + 15 = 12 + 15
→ 11x = 27
Step 3: Solve for x
Now divide both sides by 11 to solve for x:
x = 27 ÷ 11
x = 27/11
This is the exact solution. As a decimal, x ≈ 2.45, but the simplified fractional form 27/11 is preferred in most mathematical contexts for precision.
