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

Understanding the Context

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

$60 + x = 0.5(200 + x)$

Key Insights

Step 4: Solve for x

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

Final Answer

✅ x = 80

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Final Thoughts

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.

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.

Practice Problem

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

Answer:
x = 80