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Chapter 8: Problem 10

In the following exercises, solve each equation. $$ m+7.9=11.6 $$

Short Answer

Expert verified
m = 3.7

Step by step solution

01

Identify the equation

The given equation is: \[ m + 7.9 = 11.6 \]
02

Isolate the variable

To solve for \( m \), we need to isolate it on one side of the equation. Subtract 7.9 from both sides of the equation: \[ m + 7.9 - 7.9 = 11.6 - 7.9 \]
03

Simplify both sides

Simplify the left side of the equation: \[ m = 11.6 - 7.9 \] Calculate the right side: \[ m = 3.7 \]

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Key Concepts

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

solving linear equations
Solving linear equations might seem tricky at first, but it's all about understanding the process and practicing. A linear equation is an equation of the first degree, meaning it has no exponents greater than one. In our example, the equation is defined as: m + 7.9 = 11.6.
To solve this equation, we need to find the value of m that makes the equation true.
In general, solving linear equations involves the following steps: * Simplify both sides of the equation if needed * Isolate the variable using basic arithmetic operations. This method works for any simple linear equation, and understanding it is crucial for more advanced topics in algebra.
isolating variables
To solve the equation for m, we must isolate this variable on one side of the equation. Here, the equation is: equation given earlier: m + 7.9 = 11.6. To isolate m, we need to get rid of the 7.9 that is added to it. We do this by performing the opposite operation, which is subtraction.
Thus, we subtract 7.9 from both sides of the equation: m + 7.9 - 7.9 = 11.6 - 7.9.
This simplifies to: m = 11.6 - 7.9. By isolating the variable, we have simplified the equation to find that m equals 3.7.
basic arithmetic operations
Basic arithmetic operations are foundational when solving any equation. They include addition, subtraction, multiplication, and division. In this example, we primarily use subtraction.
The original equation is: m + 7.9 = 11.6. To solve for m, we subtract 7.9 from both sides. So, it looks like this: 11.6 - 7.9. This is a basic subtraction problem:
When subtracting 7.9 from 11.6, we find that m equals 3.7: 11.6 - 7.9 = 3.7. This shows how basic arithmetic operations help in isolating the variable and solving linear equations efficiently.

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