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Chapter 5: Problem 39

Solve by first clearing decimals. $$4.2=3-0.002 m$$

Short Answer

Expert verified
m = -600

Step by step solution

01

Recognize the Equation

The given equation is: \[ 4.2 = 3 - 0.002m \]
02

Clear the Decimals

Multiply every term in the equation by 1000 (the smallest power of 10 that clears all decimals): \[ 1000 \times 4.2 = 1000 \times 3 - 1000 \times 0.002m \] This simplifies to: \[ 4200 = 3000 - 2m \]
03

Isolate the Variable

Rearrange the equation to solve for \( m \): \[ 4200 - 3000 = -2m \] Simplifying, we get: \[ 1200 = -2m \]
04

Solve for m

Divide both sides of the equation by \( -2 \) to find the value of \( m \): \[ \frac{1200}{-2} = m \] Therefore, \[ m = -600 \]

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Key Concepts

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

Clearing Decimals in an Equation
When dealing with decimals in an equation, clearing them can simplify calculations. Start by finding the smallest power of 10 that can turn all decimals into whole numbers. For example, in the equation \( 4.2 = 3 - 0.002m \), the smallest power of 10 is 1000. Multiply every term in the equation by this number. This will eliminate the decimals: \[ 1000 \times 4.2 = 1000 \times 3 - 1000 \times 0.002m \] Simplifying, you'll get: \[ 4200 = 3000 - 2m \] This step makes the equation easier to solve.
Isolating the Variable
After clearing the decimals, the next step is to isolate the variable. This typically means getting the variable term on one side of the equation and constants on the other. From our transformed equation \( 4200 = 3000 - 2m \), you'll want to move the constants away from the variable term: \[ 4200 - 3000 = -2m \] Simplifying, you get: \[ 1200 = -2m \] Next, to isolate \( m \), divide both sides by -2: \[ \frac{1200}{-2} = m \] This step leaves you with the isolated variable.
Solving Linear Equations
Now we solve for the variable. With \[ \frac{1200}{-2} = m \], performing the calculation on the left side: \[ m = -600 \] This is your solution. Solving linear equations typically involves these steps: eliminating decimals, isolating the variable, and then performing any remaining mathematical operations. This method works efficiently for equations of this type.

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