x + (x+2) + (x+4) = 90 → 3x + 6 = 90 → 3x = 84 → x = 28. - Decision Point
Solving the Linear Equation: How to Solve x + (x + 2) + (x + 4) = 90 Step by Step
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
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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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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.
