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Chapter 1: Problem 37

Solve each equation, if possible. $$ 0.2 m=0.9+0.5 m $$

Short Answer

Expert verified
m = -3

Step by step solution

01

Start by isolating the variable

Subtract 0.5m from both sides of the equation to get all terms involving m on one side:\[0.2m - 0.5m = 0.9\]
02

Simplify the expression

Combine like terms to simplify the equation:\[-0.3m = 0.9\]
03

Solve for m

Divide both sides of the equation by -0.3 to isolate m:\[m = \frac{0.9}{-0.3}\]Simplify the right-hand side to get:\[m = -3\]

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Key Concepts

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

Isolating Variables
To solve an equation, one of the first steps is often isolating the variable. This means you want to get the variable (in this case, **m**) by itself on one side of the equation. In our exercise, we started with the equation: 0.2m = 0.9 + 0.5mWe isolate **m** by moving **0.5m** to the other side. To do this, subtract **0.5m** from both sides:0.2m - 0.5m = 0.9This step gives you all terms involving **m** on one side of the equation. This is important because it simplifies the problem, making it easier to solve the equation in later steps.
Combining Like Terms
After isolating the variable, the next step often involves combining like terms. Like terms are terms that have the same variables raised to the same power. In our case, both **0.2m** and **-0.5m** are like terms. So, we combine them:0.2m - 0.5m = 0.9Simplifying this gives us: -0.3m = 0.9Combining like terms helps by reducing the number of terms in the equation, making it simpler and more manageable to solve.
Simplifying Expressions
Simplifying expressions means making them as simple and straightforward as possible. In our problem, we simplified the expression by combining like terms, which resulted in:-0.3m = 0.9This simplification allows us to focus more easily on isolating the variable. With fewer terms and a simpler equation, the path to finding the value of **m** becomes clearer. This step is crucial for making the equation easier to solve.
Dividing Equations
Finally, to solve for the variable, we may need to divide both sides of the equation by a number. In our example, we had the equation:-0.3m = 0.9To isolate **m**, divide both sides by **-0.3**:m = \( \frac{0.9}{-0.3} \)By performing this division, we find:m = -3Dividing both sides by a number is often the final step in solving for the variable. It gives the exact value of the variable, completing the solution to the equation.

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