Solving the Linear Equation: How to Solve x + (x + 2) + (x + 4) = 90 Step by Step

Learning how to solve a simple linear equation is a fundamental skill in algebra, essential for mastering more advanced math concepts. One common type of problem involves combining like terms and isolating the variable using basic algebraic operations. In this article, we’ll walk through solving the equation:

x + (x + 2) + (x + 4) = 90
to find the value of x.

Understanding the Context

Why Solving Linear Equations Matters

Linear equations like this form the foundation of algebra. They appear in everyday problems, science, engineering, and finance. Understanding how to solve them step-by-step empowers students, professionals, and lifelong learners alike.

Step 1: Combine Like Terms

Start with the original equation:
x + (x + 2) + (x + 4) = 90

Notice that there are three terms containing x and two constant terms:

  • x + x + x = 3x
  • 2 + 4 = 6
x + (x+2) + (x+4) = 90 → 3x + 6 = 90 → 3x = 84 → x = 28.

Key Insights

Adding these together gives:
3x + 6 = 90

This simplification is key—turning complexity into clarity.

Step 2: Isolate the Variable

Next, subtract 6 from both sides to eliminate the constant term on the left:
3x + 6 − 6 = 90 − 6
→ 3x = 84

This step relies on the concept of equality: whatever operation you perform on one side, you must do to the other.

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Final Thoughts

Step 3: Solve for x

Now divide both sides by 3:
3x ÷ 3 = 84 ÷ 3
→ x = 28

This final step isolates x, giving us the solution.

Final Verification

It’s always wise to plug the answer back into the original equation:
x + (x + 2) + (x + 4) = 90
→ 28 + (28 + 2) + (28 + 4) = 28 + 30 + 32 = 90 ✔️

The equation holds true, confirming our solution.

Summary

The equation x + (x + 2) + (x + 4) = 90 simplifies using like terms, isolates the variable, and solves cleanly to x = 28. This method—combining terms, isolating x, and verifying—builds a strong framework for tackling all linear equations.

Related Topics

  • How to simplify expressions with parentheses
  • Understanding linear equations and their real-world applications
  • Step-by-step guide to solving two-step equations

Mastering these basics will make advanced math far more approachable—and far more fun.