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Chapter 3: Problem 29

Solve the equation using the multiplication or division properties of equality. $$5 m=0$$

Short Answer

Expert verified
m = 0.

Step by step solution

01

- Understand the equation

The equation given is 5m = 0. The goal is to isolate the variable m.
02

- Apply the division property of equality

To isolate m, divide both sides of the equation by 5.
03

- Simplify the equation

Dividing both sides of 5m = 0 by 5 gives \( \frac{5m}{5} = \frac{0}{5} \).
04

- Calculate the result

\( m = 0 \). Dividing zero by any non-zero number still results in zero.

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Key Concepts

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

solving equations
Solving equations is a fundamental concept in algebra. The process involves finding the value of the variable that makes the equation true. To solve an equation, you typically perform operations to isolate the variable on one side of the equation. Here is the step-by-step breakdown for solving an equation like the one given:

First, understand the equation: The given equation is 5m = 0. Our aim is to find the value of 'm'. To find this, we need to get 'm' by itself.

Next, apply the division property of equality (explained in the next section). Finally, simplify and solve for 'm'. Remember, practice makes perfect, so work through each step methodically.
division property
The division property of equality is a tool used for solving equations. It states that if you divide both sides of an equation by the same non-zero number, both sides remain equal.

Here鈥檚 the application in our example:
  • Start with the equation 5m = 0.
  • To isolate 'm', divide both sides by 5 (the coefficient of m).
  • This gives \(\frac{5m}{5} = \frac{0}{5}\).
  • Simplifying that, we find that m = 0.

This method is very powerful in solving linear equations, especially when you need to isolate the variable.
isolate variable
To solve any equation, one of the key steps is to isolate the variable. Isolating the variable means getting the variable by itself on one side of the equation. Here are some tips on how to do it effectively:

  • Look at the equation and identify the variable you need to isolate. In our example, it鈥檚 'm'.
  • Use operations like addition, subtraction, multiplication, or division to move other terms away from the variable. For example, in 5m = 0, we used division to separate m from 5.
  • After isolating the variable, simplify the equation if necessary to get your answer.

Isolating the variable makes it easier to solve the equation and understand the relationship between the quantities involved.

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