\[ 60 + x = 0.5(200 + x) \] - Imagemakers
Solving the Equation: 60 + x = 0.5(200 + x)
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
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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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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
