\[ 6b - 3 + 4b = 12 \] - Decision Point
Solving the Equation: 6b – 3 + 4b = 12 – A Complete Step-by-Step Guide
Solving the Equation: 6b – 3 + 4b = 12 – A Complete Step-by-Step Guide
If you’re tackling math problems like the equation 6b – 3 + 4b = 12, you’re in the right place. This article breaks down how to solve linear equations step-by-step, explaining key algebraic concepts along the way. Understanding how to solve equations like this is essential for algebra learners, students, and anyone looking to strengthen their problem-solving skills.
Understanding the Context
What Is the Equation: 6b – 3 + 4b = 12?
The equation 6b – 3 + 4b = 12 is a linear equation in one variable, specifically b. Such equations involve terms with the variable (in this case, b), constant numbers, and basic arithmetic operations. Solving them means finding the value of b that makes both sides of the equation equal.
Step-by-Step Solution
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Key Insights
Step 1: Combine Like Terms
Start by combining the terms containing b:
✅ 6b + 4b = 10b
So the equation becomes:
10b – 3 = 12
Step 2: Isolate the Variable Term
Next, eliminate the constant term by adding 3 to both sides:
10b – 3 + 3 = 12 + 3
⇒ 10b = 15
Step 3: Solve for b
Now divide both sides by 10:
b = 15 ÷ 10 = 3/2 = 1.5
Verification – Check Your Answer
Plug b = 1.5 back into the original equation:
Left side: 6(1.5) – 3 + 4(1.5) = 9 – 3 + 6 = 12
Right side: 12
✔️ The equation holds true, confirming our solution.
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Why Solving Linear Equations Matters
Linear equations form the foundation for more advanced math topics like systems of equations, graphing, and real-world problem modeling. Knowing how to solve equations like 6b – 3 + 4b = 12 helps you:
- Simplify and interpret mathematical expressions
- Solve word problems involving successions or budget planning
- Prepare for algebra, calculus, and engineering applications
Tips for Solving Similar Equations
- Combine like terms first to simplify the equation.
- Use inverse operations to isolate the variable.
- Always verify your solution by substituting back into the original equation.
- Practice with positive, negative, and fractional coefficients for confidence.
Conclusion
The equation 6b – 3 + 4b = 12 is a straightforward example of solving a linear equation using basic algebra. By combining like terms and isolating the variable step-by-step, we find that b = 1.5 is the solution. This process not only solves the problem but builds a strong foundation in algebraic reasoning. With consistent practice, these skills will become second nature—empowering you to tackle increasingly complex math challenges with confidence.
