Equation: 0.2x + 0.8(5 - x) = 0.5 * 5 - Decision Point
Solving the Linear Equation: 0.2x + 0.8(5 - x) = 0.5 × 5 – A Step-by-Step Guide
Solving the Linear Equation: 0.2x + 0.8(5 - x) = 0.5 × 5 – A Step-by-Step Guide
Understanding linear equations is a fundamental skill in algebra, essential for students and professionals alike. One commonly encountered equation is:
0.2x + 0.8(5 - x) = 0.5 × 5
Understanding the Context
In this comprehensive article, we’ll break down this equation step-by-step, solve it clearly, and explore its real-world applications. Whether you're preparing for exams, teaching algebra, or solving practical problems, this guide will help you master the equation.
Understanding the Equation
The equation
0.2x + 0.8(5 - x) = 0.5 × 5
combines linear expressions involving a variable x and arithmetic operations. Let's rewrite and simplify each side to clarify the problem.
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Key Insights
First, simplify the right-hand side:
0.5 × 5 = 2.5
So, the equation becomes:
0.2x + 0.8(5 - x) = 2.5
Step 1: Expand the Parentheses
Distribute 0.8 across (5 - x):
0.8 × 5 = 4
0.8 × (-x) = -0.8x
Thus:
0.2x + (4 - 0.8x) = 2.5
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Step 2: Combine Like Terms
Combine the x terms:
0.2x - 0.8x = -0.6x
So:
-0.6x + 4 = 2.5
Step 3: Isolate the Variable Term
Subtract 4 from both sides:
-0.6x = 2.5 - 4
-0.6x = -1.5
Step 4: Solve for x
Divide both sides by -0.6:
x = -1.5 / (-0.6) = 2.5
