x + 300 = 1.2x + 180 - Silent Sales Machine

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

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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Final Thoughts

$$
300 - 180 = 0.2x + 180 - 180
$$

$$
120 = 0.2x
$$

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:
$$
1.2x + 180 = 1.2(600) + 180 = 720 + 180 = 900
$$