7(0) + 3(2) + c = 7 \Rightarrow 6 + c = 7 \Rightarrow c = 1. - Veritas Home Health

Understanding the Context

At first glance, this may appear straightforward, but solving it reveals fundamental principles of algebra and mathematical reasoning. In this article, we’ll break down how this equation resolves to c = 1, why it matters, and how to approach similar algebraic expressions with confidence.

Step-by-Step Breakdown: How We Solve 7(0) + 3(2) + c = 7

Let’s go through the logic methodically to uncover the value of c.

Key Insights

Step 1: Simplify Both Sides of the Equation

Start by simplifying expressions on the left-hand side:

• 7(0) = 0
  
• 3(2) = 6
  
• So the equation becomes:
  0 + 6 + c = 7

Step 2: Combine Like Terms

Adding 0 and 6 gives:

6 + c = 7

This simplification is crucial—it brings the equation into a clearer form, isolating the unknown variable.

Final Thoughts

Step 3: Isolate c to Solve for It

To find c, subtract 6 from both sides:

6 + c − 6 = 7 − 6
→ c = 1

Why This Equation Matters: Mathematical Clarity and Problem Solving

While 7(0) + 3(2) + c = 7 might seem unremarkable, working through it exemplifies key algebraic strategies:

• Order of Operations: Multiplication (7 × 0 and 3 × 2) precedes addition, followed by isolation of the variable.
  
• Simplification: Reducing expressions makes patterns clearer.
  
• Logical Isolation: Subtracting known values to solve for unknowns is a cornerstone of equation solving.