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 Context

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.

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

Key Insights

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

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Final Thoughts

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.