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 Γ— 5 = 10
The equation becomes:
10 + 3b = 11

Solved 2.11. Show that: (a) If event A implies B, and B | Chegg.com

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Solved 2.11. Show that: (a) If event A implies B, and B | Chegg.com
Solved: Simplify the following expression. -2+5(a-2b+1)-3(8-2a+b) 3a-b ...
Solved Suppose B={(-3,5),(11,2)} ο»Ώand B'={(2,5),(7,1)}.a. | Chegg.com
Solved 6 – 4 3 -5 1- Let A= 11:1-11 and B= 8 – 1 3 5 Find – | Chegg.com
Solved (a12b113b53c23)74 | Chegg.com

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 βˆ’ 10 = 11 βˆ’ 10
3b = 1

Step 3: Solve for b

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

Final Answer:

b = 1/3

Continue Reading

To solve the inequality \( x^3 - 4x^2 + x + 6 < 0 \), we first find the roots of the cubic polynomial \( x^3 - 4x^2 + x + 6 = 0 \).
Using the Rational Root Theorem, we test possible rational roots: \( \pm 1, \pm 2, \pm 3, \pm 6 \).
\[ 1^3 - 4(1)^2 + 1 + 6 = 1 - 4 + 1 + 6 = 4

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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 β€” 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 β€” like subtraction before division β€” makes complex problem-solving more manageable.

Summary

Solving 2(5) + 3b = 11:

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