2(3) + 3d = 15 \implies 3d = 9 \implies d = 3 - Coaching Toolbox
Solving the Equation: 2(3) + 3d = 15 Implies d = 3
An Easy Step-by-Step Explanation
Solving the Equation: 2(3) + 3d = 15 Implies d = 3
An Easy Step-by-Step Explanation
Understanding basic algebra is essential for solving equations confidently. One commonly encountered expression is 2(3) + 3d = 15, which many students solve step-by-step to determine that d = 3. This article explores how this equation is solved, why it works, and why mastering such problems enhances mathematical fluency.
Understanding the Context
What Does the Equation 2(3) + 3d = 15 Mean?
The equation 2(3) + 3d = 15 combines arithmetic and variables to form a linear relationship. At first glance, it includes constants and a variable term 3d, but simplifying known parts makes it easier to isolate d.
Step-by-Step Solution: From 2(3) + 3d = 15 to d = 3
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Key Insights
Step 1: Simplify the Constant Term
Start by calculating any multiplication on the left side:
2(3) = 6, so the equation becomes:
6 + 3d = 15
Step 2: Isolate the Variable Term
Subtract 6 from both sides to remove the constant:
3d = 15 – 6 → 3d = 9
Step 3: Solve for d
To find d, divide both sides by 3:
d = 9 ÷ 3 → d = 3
Why This Process Works (Conceptual Understanding)
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Every step follows fundamental rules of algebra:
- Multiplication is commutative, so 2(3) = 3(2) = 6
- Equality preserves balance — operations applied to both sides keep the equation true
- Isolating variables allows direct value determination
This structure ensures the solution d = 3 satisfies the original equation:
Plugging back: 2(3) + 3(3) = 6 + 9 = 15
Why Learning This Matters
Mastering simple algebraic manipulations builds confidence and paves the way for tackling more complex equations. Recognizing patterns like combining constants first, then isolating the variable, is a skill used throughout math, science, and engineering.
Final Thoughts
The equation 2(3) + 3d = 15 leads directly to d = 3 through clear, logical steps:
- Simplify → 6 + 3d = 15
- Simplify further → 3d = 9
- Divide → d = 3
By practicing such steps, anyone can solve similar equations with clarity and precision.
