x + 300 = 1.2x + 180
Solving the Equation x + 300 = 1.2x + 180: A Step-by-Step Guide
Understanding how to solve linear equations is a fundamental skill in algebra, and equations like x + 300 = 1.2x + 180 are excellent examples to practice this concept. Whether you’re a student or just brushing up on your math skills, solving this equation step-by-step will help you build strong problem-solving abilities.
Understanding the Equation
The equation x + 300 = 1.2x + 180 is a linear equation involving one variable, x. Our goal is to isolate x on one side of the equation to find its exact value. This process reinforces important algebra techniques and strengthens logical thinking.
Step-by-Step Solution
Step 1: Eliminate the variable on one side Start by subtracting x from both sides to collect all x terms on the right:
$$ x + 300 - x = 1.2x + 180 - x $$
This simplifies to: $$ 300 = 0.2x + 180 $$
Step 2: Isolate the constant terms Subtract 180 from both sides to move all constants to the left:
$$ 300 - 180 = 0.2x + 180 - 180 $$
$$ 120 = 0.2x $$
Step 3: Solve for x Now divide both sides by 0.2 to solve for x:
$$ x = rac{120}{0.2} = 600 $$
Verification
To ensure the solution is correct, substitute x = 600 back into the original equation:
Left side: $$ x + 300 = 600 + 300 = 900 $$
Right side: $$ 1.2x + 180 = 1.2(600) + 180 = 720 + 180 = 900 $$
Both sides equal 900, confirming that our solution is accurate.
Why This Equation Matters
Equations like x + 300 = 1.2x + 180 illustrate key algebraic principles: combining like terms, isolating variables, and using inverse operations. These concepts apply broadly across math, science, engineering, and economics—making mastery essential for future learning.
Tips for Solving Similar Equations
- Stay organized: Write each step clearly to avoid mistakes.
- Use inverse operations: Add/subtract to isolate variables; multiply/divide to eliminate coefficients.
- Check your work: Substitute your solution back into the original equation.
- Keep decimals in check: Rewrite decimals as fractions or whole numbers when possible (e.g., 0.2 = 1/5) to simplify calculations.
Final Answer
$$ oxed{x = 600} $$
By mastering equations like x + 300 = 1.2x + 180, you gain confidence in handling variables, solving real-world problems, and preparing for advanced mathematics. Keep practicing—algebra is the foundation of many powerful tools!
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