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Chapter 2: Problem 37

Solve using the addition principle. Don't forget to check! $$ m+3.9=5.4 $$

Short Answer

Expert verified
m = 1.5

Step by step solution

01

- Define the equation

Start with the given equation: \[ m + 3.9 = 5.4 \]
02

- Isolate the variable

To isolate the variable \( m \), subtract 3.9 from both sides of the equation: \[ m + 3.9 - 3.9 = 5.4 - 3.9 \]
03

- Simplify the equation

Simplify both sides to solve for \( m \): \[ m = 1.5 \]
04

- Check the solution

Substitute \( m = 1.5 \) back into the original equation to verify: \[ 1.5 + 3.9 = 5.4 \] Both sides equal 5.4, so the solution is correct.

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Key Concepts

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

Addition Principle
The addition principle is fundamental for solving linear equations. It states that you can add or subtract the same value from both sides of the equation without changing its equality. This principle helps to systematically isolate variables and solve equations.
For our exercise, we have the equation: \( m + 3.9 = 5.4 \).
Using the addition principle, if we want to eliminate the constant term on one side, we subtract 3.9 from both sides. This isolates the variable term,
transforming the equation to keep it in balance:
\( m + 3.9 - 3.9 = 5.4 - 3.9 \).
Isolating Variables
Isolating the variable means getting the variable alone on one side of the equation. This step is crucial to solve for the unknown.
For our exercise, the variable we isolate is \( m \).
Starting with \( m + 3.9 - 3.9 = 5.4 - 3.9 \),
we simplify both sides:
\ m = 5.4 - 3.9 \.
Simplifying further, we get
\ m = 1.5 \.
Now, \( m \) is isolated, and we find \( m = 1.5 \).
Checking Solutions
Checking your solutions confirms accuracy. To check \( m = 1.5 \) for our equation \( m + 3.9 = 5.4 \), substitute \ m \ back into the original equation.
Replace \( m \) with 1.5:
\ 1.5 + 3.9 = 5.4 \.
If both sides of the equation match, the solution is correct.
Here, \ 1.5 + 3.9 = 5.4 \ holds true, verifying our solution.
This step ensures your solution accurately satisfies the original equation.

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