Equation: x + (x + 2) + (x + 4) = 90
Solving the Equation: x + (x + 2) + (x + 4) = 90
Mathematics may seem daunting at times, but equations like x + (x + 2) + (x + 4) = 90 reveal how logic and algebra simplify real-world problems. In this article, we break down how to solve this equation step-by-step, explore its meaning, and show why understanding such equations is valuable in both school and daily life. Whether you're a student preparing for exams, a teacher designing lessons, or someone simply curious about problem-solving, this guide offers clear insights into solving one of the most common linear equations.
What Is the Equation?
The equation you’ll explore is:
x + (x + 2) + (x + 4) = 90
At first glance, it might look complex because of the parentheses, but a closer look reveals it’s a simple linear equation. By combining like terms and isolating the variable, we uncover the value of x, the unknown key to balancing both sides.
Step-by-Step Solution
To solve x + (x + 2) + (x + 4) = 90, follow these straightforward algebraic steps:
Step 1: Remove Parentheses and Combine Like Terms
First, expand the expression inside the parentheses and collect all x-terms and constant terms on the left side: x + x + 2 + x + 4 = 90 Combine like terms: ( x + x + x ) + (2 + 4) = 90 3x + 6 = 90
Step 2: Isolate the Variable
Subtract 6 from both sides to move constants to the right: 3x = 90 - 6 3x = 84
Step 3: Solve for x
Divide both sides by 3: x = 84 ÷ 3 x = 28
What Does x = 28 Mean?
Substitute x = 28 back into the original equation to verify: 28 + (28 + 2) + (28 + 4) = 28 + 30 + 32 = 90 ✔️
This confirms the solution. The equation balances exactly when x equals 28, transforming left-side terms into a total of 90 through simple arithmetic and algebraic simplification.
Why This Equation Matters
Understanding how to solve equations like x + (x + 2) + (x + 4) = 90 builds foundational algebra skills. Real-world applications include:
- Budgeting: Comparing incremental expenses.
- Physics: Calculating motion with equally spaced time intervals.
- Education: Designing smart age or score problems.
Mastering step-by-step solving fosters logical thinking and problem-solving confidence, valuable in STEM fields, data analysis, and daily decision-making.
Practice & Further Exploration
Want to strengthen your skills? Try variations like:
- 2x + (x + 3) + (x + 6) = 60
- Or solve for x in multi-step expressions involving fractions or decimals.
Online math tools, apps, and worksheets provide endless practice problems to refine your algebraic intuition.
Summary
- Equation: x + (x + 2) + (x + 4) = 90
- Solution: x = 28
- Why it matters: A gateway to understanding linear relationships and logical reasoning
- Next steps: Explore similar equations, apply algebra to real problems, and share your newfound knowledge!
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Equation-solving isn’t just for classrooms—it’s a powerful skill to decode patterns and solve problems confidently. Start with simple expressions, build your fluency, and watch how mathematics transforms challenges into clear, satisfying answers.
