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