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Chapter 2: Problem 133

Solve each equation. $$m-41=-14$$

Short Answer

Expert verified
m = 27

Step by step solution

01

- Identify the Equation

The equation given is \( m - 41 = -14 \)
02

- Isolate the Variable

To solve for \( m \), add 41 to both sides of the equation to get: \( m - 41 + 41 = -14 + 41 \)
03

- Simplify both sides

Simplify the equation to find the value of \( m \): \( m = 27 \)

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Key Concepts

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

Isolating Variables
In algebra, isolating the variable means getting the variable by itself on one side of the equation. This is a crucial step in solving any linear equation. Let's break it down with our given problem:

We start with the equation: \( m - 41 = -14 \)

To isolate the variable \( m \), we need to eliminate the constant number on the same side as \( m \). Here, that constant is -41. We do this by performing the inverse operation. Since -41 is being subtracted from \( m \), we add 41 to both sides of the equation:

  • Original equation:

    \( m - 41 = -14 \)
  • Add 41 to both sides:
    \( m - 41 + 41 = -14 + 41 \)
By adding the same number to both sides, we maintain the balance of the equation. Now let's simplify!
Simplifying Equations
Simplifying means performing the necessary operations to make the equation look simpler, often resulting in a direct answer.

After isolating the variable on one side, we have:

  • Simplified equation:

    \( m - 41 + 41 = -14 + 41 \)
The opposite numbers \( -41 \) and \( 41 \) cancel each other out on the left side, leaving us with:

  • After cancellation:
    \( m = -14 + 41 \)
Next, we perform the arithmetic on the right side:

  • Calculate the sum:

    \( m = 27 \)
By simplifying both sides, we arrive at the solution!
Basic Algebra Steps
Solving linear equations often involves a series of basic algebra steps. Here's a quick review of the process we used in the example problem:

  • Identify the equation:

    Start with the given equation. For example: \( m - 41 = -14 \)

  • Isolate the variable:

    Use inverse operations such as addition, subtraction, multiplication, or division to move constants to the other side of the equation. Add 41 to both sides:

    \( m - 41 + 41 = -14 + 41 \)

  • Simplify:

    Perform the necessary arithmetic operations:

    \( m = 27 \)
Knowing these basic steps helps make solving algebra problems easier and quicker. Remember to perform each step carefully to avoid mistakes. Practice these steps often, and soon you'll solve linear equations with confidence!

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