\[ 2x + 9x - 15 = 12 \] - Decision Point
Solving the Linear Equation: 2x + 9x - 15 = 12 – A Step-by-Step Guide
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.
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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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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.
