Solving the Equation 2(5) + 3b = 11 Step-by-Step: Find b and Understand the Process

Understanding how to solve linear equations is a fundamental skill in algebra, essential for students, educators, and anyone working with mathematical modeling. Today, we’ll break down the equation 2(5) + 3b = 11, simplify it step-by-step, and arrive at the solution b = 1/3. This clear explanation helps clarify not just the answer, but the logical process behind it.

Understanding the Context

The Given Equation

Start with the equation:
2(5) + 3b = 11

Step 1: Perform the Multiplication

Multiply 2 by 5:
2 × 5 = 10
The equation becomes:
10 + 3b = 11

$2(5) + 3b = 11 \implies 10 + 3b = 11 \implies b = \frac{1}{3}$

Key Insights

Step 2: Isolate the Variable Term

To solve for b, we first eliminate the constant on the left side. Subtract 10 from both sides:
10 + 3b − 10 = 11 − 10
3b = 1

Step 3: Solve for b

Now, divide both sides by 3 to isolate b:
b = 1 ÷ 3
b = 1/3

Final Answer:

b = 1/3

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Final Thoughts

Why This Process Matters

Breaking down an equation step-by-step helps prevent errors and builds stronger algebra skills. Each operation follows the rules of equality — whatever you do to one side of the equation, you must do to the other to keep it balanced.

Understanding simplification, order of operations, and inverse operations — like subtraction before division — makes complex problem-solving more manageable.

Summary

Solving 2(5) + 3b = 11:

Multiply: 2(5) = 10
Subtract: 3b = 1
Divide: b = 1/3

This realization gives us:
b = 1/3, a simple yet powerful solution revealing the unknown variable’s exact value.

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Step-by-step guide solving 2(5) + 3b = 11, simplifying to 10 + 3b = 11, then solving for b to get b = 1/3. Learn algebra fundamentals with clear, accurate steps.