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Chapter 2: Problem 93

Solve each equation. $$ 0.06 x=300 $$

Short Answer

Expert verified
x = 5000

Step by step solution

01

Identify the Equation

The given equation is \[ 0.06 x = 300 \]
02

Isolate the Variable

To solve for \( x \), divide both sides of the equation by 0.06 to get:\[ x = \frac{300}{0.06} \]
03

Simplify the Right Side

Calculate the right side of the equation:\[ x = \frac{300}{0.06} = 5000 \]
04

Verify the Solution

To ensure the solution is correct, substitute \( x = 5000 \) back into the original equation and check if the left side equals the right side:\[0.06 \times 5000 = 300 \]Since both sides are equal, the solution is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolate the Variable
To solve linear equations, the primary goal is to isolate the variable. This means you need to get the variable by itself on one side of the equation.
In the given equation \( 0.06 x = 300 \), we need to solve for \( x \).
Here's how you can isolate the variable step-by-step:
  • First, identify the coefficient multiplied by \( x \). In this case, it is \( 0.06 \).
  • Next, to get \( x \) by itself, divide both sides of the equation by \( 0.06 \). This operation removes the coefficient from the variable.
  • So, you will perform the division: \[ x = \frac{300}{0.06} \]
This technique ensures that you have successfully isolated the variable.
Simplify Fractions
After isolating the variable, you often need to simplify fractions. Simplifying fractions will make the solution clearer and easier to understand.
In our equation \( x = \frac{300}{0.06} \), the fraction can be simplified. Follow these steps:
  • First, perform the division operation. Divide 300 by 0.06.
  • This computation results in \( x = 5000 \).
Simplifying fractions can sometimes involve finding a common denominator or reducing the numerator and denominator by a common factor. But in this case, simple division gives us the final value for \( x \).
Verify the Solution
Verification is a critical step in solving linear equations. To verify the solution, substitute the value of the variable back into the original equation and ensure that both sides of the equation are equal.
For our solution, we found \( x = 5000 \). Let's substitute this back into the original equation \( 0.06 x = 300 \):
  • Substitute \( x \) with 5000, so the equation becomes: \[ 0.06 \times 5000 = 300 \]
  • Perform the multiplication: \[ 300 = 300 \]
Since both sides of the equation are equal, this confirms our solution is correct.
Always remember to verify your solutions to confirm their accuracy. This step helps catch any mistakes that might have occurred during the equation solving process.

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