x + 300 = 1.2x + 180 - Richter Guitar
Solving the Equation x + 300 = 1.2x + 180: A Step-by-Step Guide
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 Context
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
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Key Insights
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:
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$$
300 - 180 = 0.2x + 180 - 180
$$
$$
120 = 0.2x
$$
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:
$$
1.2x + 180 = 1.2(600) + 180 = 720 + 180 = 900
$$
