Simplify: 0.2x + 4 - 0.8x = 2.5 - Richter Guitar
Simplify 0.2x + 4 - 0.8x = 2.5: A Step-by-Step Solution
Simplify 0.2x + 4 - 0.8x = 2.5: A Step-by-Step Solution
Solving linear equations is a fundamental skill in algebra, and understanding how to simplify expressions like 0.2x + 4 - 0.8x = 2.5 can make complex problems much easier to manage. Whether you're a student learning algebra or simply looking to improve your math skills, simplifying this equation step-by-step is key to mastering equation solving.
What Is the Equation?
Understanding the Context
We start with:
0.2x + 4 - 0.8x = 2.5
This expression involves combining like terms, isolating the variable x, and solving for its value — all essential steps in simplifying linear equations.
Step 1: Combine Like Terms
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Key Insights
The left-hand side contains two terms with x: 0.2x and -0.8x. Combine these:
(0.2x - 0.8x) + 4 = 2.5
→ -0.6x + 4 = 2.5
Combining the coefficients gives -0.6x, simplifying the left-hand side.
Step 2: Isolate the Variable Term
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Subtract 4 from both sides to move the constant to the right:
-0.6x = 2.5 - 4
-0.6x = -1.5
This step eliminates the constant, bringing cumbersome numbers close to zero for easier division.
Step 3: Solve for x
Now divide both sides by -0.6:
x = -1.5 / (-0.6)
x = 2.5
Final Answer:
x = 2.5
This solution confirms that when you simplify 0.2x + 4 - 0.8x = 2.5, you arrive cleanly at x = 2.5.
