\[ 2x + 9x - 15 = 12 \]

February 22, 2026

$2x + 9x - 15 = 12$

Solving the Linear Equation: 2x + 9x - 15 = 12 – A Step-by-Step Guide

Solving equations is a fundamental skill in algebra, essential for students, educators, and anyone working in math-intensive fields. One commonly encountered type is the linear equation, such as 2x + 9x – 15 = 12. Whether you're preparing for exams, teaching algebra, or simply brushing up on math fundamentals, understanding how to solve this equation can boost your confidence and problem-solving skills.

This article provides a clear, detailed breakdown of solving 2x + 9x - 15 = 12, including step-by-step instructions, simplification techniques, and practical applications.

Understanding the Equation

Start with the equation: 2x + 9x – 15 = 12

This is a linear equation in one variable, x. Linear equations feature variables raised to the first power only, making them relatively straightforward to solve using inverse operations.

Step 1: Combine Like Terms

The first step in simplifying the equation is combining like terms — specifically, the terms involving x:

2x + 9x = 11x

So the equation becomes: 11x – 15 = 12

Step 2: Isolate the Variable Term

To solve for x, isolate the term with the variable. Add 15 to both sides of the equation:

11x – 15 + 15 = 12 + 15 → 11x = 27

Step 3: Solve for x

Now divide both sides by 11 to solve for x:

x = 27 ÷ 11 x = 27/11

This is the exact solution. As a decimal, x ≈ 2.45, but the simplified fractional form 27/11 is preferred in most mathematical contexts for precision.

Why This Equation Matters

At first glance, 2x + 9x – 15 = 12 might look simple, but mastering such equations builds a foundation for more complex topics like systems of equations, word problems, and real-world modeling (e.g., budgeting, distance-over-time problems).

Tips for Solving Linear Equations

Always combine like terms first to simplify.
Use inverse operations to isolate variables.
Perform the same operation on both sides to maintain equation balance.
Simplify fractions when possible for clarity.

Final Answer

The solution to the equation 2x + 9x – 15 = 12 is: x = 27/11

Additional Resources

If you're looking to strengthen your algebra skills, explore:

Graphing linear equations
Solving double equations and inequalities
Working with real-world math problems
Using technology tools like graphing calculators or apps for equation solving

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Start solving equations today — mastering these basics unlocks a world of mathematical possibilities!