Solving the Equation: 60 + x = 0.5(200 + x)

Understanding how to solve equations is fundamental in algebra, and today we’ll tackle the equation 60 + x = 0.5(200 + x) step-by-step. Whether you’re a student learning basic algebra, a teacher explaining problem-solving techniques, or someone brushing up on math fundamentals, this article will guide you through solving linear equations with clear explanations and practical insight.

Step-by-Step Solution

The given equation is: 60 + x = 0.5(200 + x)

Step 1: Expand the Parentheses

First, distribute the 0.5 on the right-hand side: 60 + x = 0.5 × 200 + 0.5 × x 60 + x = 100 + 0.5x

Step 2: Rearrange Terms with x on One Side

Subtract 0.5x from both sides to gather like terms: 60 + x – 0.5x = 100 60 + 0.5x = 100

Step 3: Isolate the Constant

Subtract 60 from both sides: 0.5x = 100 – 60 0.5x = 40

Step 4: Solve for x

Divide both sides by 0.5: x = 40 ÷ 0.5 x = 80

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Final Answer

✅ x = 80

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Why This Equation Matters

Solving linear equations like 60 + x = 0.5(200 + x) builds essential problem-solving skills. These types of equations are commonly found in science, engineering, economics, and everyday decision-making. They help model real-world situations involving growth, cost, and balance.

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Tips for Solving Similar Equations

• Always simplify both sides using distributive property.
• Move variables to one side and constants to the other.
• Use inverse operations carefully to isolate the variable.
• Check your answer by substituting back into the original equation.

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Practice Problem

Solve: 60 + x = 0.5(200 + x)

Answer: x = 80

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References

• Algebra Fundamentals: Principles and Problem Solving
• Khan Academy – Linear Equations
• Math.com – Solving Equations with Variables on Both Sides

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Ready to master algebra? Mastering equations like 60 + x = 0.5(200 + x) opens the door to more complex math and real-world applications. Start practicing today!