800(x + 5) + 1200x = 24000
Solving the Equation: 800(x + 5) + 1200x = 24,000
Mathematics is all around us—hidden in formulas, budgets, and everyday problem-solving. Whether you're a student tackling algebra or a professional figuring out a budget, equations like 800(x + 5) + 1200x = 24,000 come up often. In this detailed SEO-friendly guide, we’ll break down how to solve this linear equation step-by-step, explain its real-world applications, and show why mastering algebra is essential.
What Is the Equation: 800(x + 5) + 1200x = 24,000?
At first glance, the equation 800(x + 5) + 1200x = 24,000 might look intimidating. But with careful expansion and simplification, it becomes manageable. This equation involves distributing a compound term, combining like terms, and isolating the variable x to find its exact value.
Step-by-Step Solution: How to Solve 800(x + 5) + 1200x = 24,000
Step 1: Expand the Parentheses Distribute the 800 across (x + 5): 800 × x = 800x 800 × 5 = 4,000 So, 800(x + 5) = 800x + 4,000
Now the equation becomes: 800x + 4,000 + 1200x = 24,000
Step 2: Combine Like Terms Combine the x terms (800x + 1200x = 2000x): 2000x + 4,000 = 24,000
Step 3: Isolate the x-Term Subtract 4,000 from both sides: 2000x = 24,000 – 4,000 2000x = 20,000
Step 4: Solve for x Divide both sides by 2000: x = 20,000 ÷ 2000 x = 10
Verification
Plug x = 10 back into the original equation: 800(10 + 5) + 1200(10) = 24,000 800(15) + 12,000 = 24,000 12,000 + 12,000 = 24,000 ✅
True—our solution works!
Real-World Applications of Linear Equations
Equations like this aren’t just abstract math—they model real-life situations:
- Budgeting: Planning monthly expenses with fixed and variable costs.
- Distance, Time, Speed: Calculating travel times when rates vary.
- Revenue Projections: Estimating income based on units sold and pricing.
- Budget Allocation: Distributing funds across departments or projects.
Mastering algebra helps you make informed decisions and solve practical problems efficiently.
Why Knowing How to Solve These Equations Matters
Beyond math class, understanding how to manipulate expressions and isolate variables equips you for:
- Data analysis in business and science.
- Programming logic, where clean algorithms depend on precise calculations.
- Critical thinking—identifying patterns and relationships in complex scenarios.
Final Thoughts
Solving 800(x + 5) + 1200x = 24,000 follows the standard algebraic process: expansion, simplification, combination, and isolation of the variable. Remembering each step builds confidence in handling equations both in exams and real life.
If you’re still struggling, keep practicing—algebra reveals the quiet logic behind the numbers we see every day.
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Mastering algebra starts with simple equations—and grows into powerful problem-solving skills. Start solving today!
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