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.

Understanding the Context

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.

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Key Insights

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

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Final Thoughts

Step 3: Solve for x

Divide both sides by 3:
 x = 84 Γ· 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 βœ”οΈ

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.