x + 300 = 0.6(x + x + 300) - Decision Point
Solving the Linear Equation: X + 300 = 0.6(X + X + 300) – A Step-by-Step Guide
Solving the Linear Equation: X + 300 = 0.6(X + X + 300) – A Step-by-Step Guide
If you’ve ever come across the equation x + 300 = 0.6(x + x + 300), you’re not alone. This seemingly simple linear expression is a great example of algebra in action — essential for students, everyday problem solvers, and anyone diving into equations.
In this article, we’ll walk through how to solve x + 300 = 0.6(x + x + 300) step-by-step, explain why the method works, and highlight practical uses of such problems in real life.
Understanding the Context
Understanding the Equation
We begin with:
x + 300 = 0.6(x + x + 300)
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Key Insights
At first glance, two identical terms — x + x — appear in the parentheses. Simplifying these helps reduce complexity.
Step 1: Simplify the Right-Hand Side
Notice that x + x = 2x, so the equation becomes:
x + 300 = 0.6(2x + 300)
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Now distribute 0.6 across the parentheses:
x + 300 = 0.6 × 2x + 0.6 × 300
x + 300 = 1.2x + 180
Step 2: Move All Terms Involving x to One Side
Subtract x from both sides:
x + 300 - x = 1.2x + 180 - x
300 = 0.2x + 180
Step 3: Isolate the Variable Term
Subtract 180 from both sides:
300 - 180 = 0.2x
120 = 0.2x
