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Chapter 2: Problem 98

Solve for \(x .\) Assume \(a, c, m \neq 0\) $$ \text { If } n+268=124, \text { find } n-268 $$

Short Answer

Expert verified
\( n - 268 = -412 \)

Step by step solution

01

- Understand the given equation

Start by analyzing the given equation: \[ n + 268 = 124 \]This equation means that when 268 is added to an unknown value \( n \), the result is 124.
02

- Solve for the variable n

To find the value of \( n \), isolate \( n \) by subtracting 268 from both sides of the equation: \[ n = 124 - 268 \]Perform the subtraction to get: \[ n = -144 \]
03

- Find the value of n - 268

Now that the value of \( n \) is known, solve for \( n - 268 \): Substitute \( n = -144 \) into the expression: \[ n - 268 = -144 - 268 \]Perform the subtraction to get: \[ n - 268 = -412 \]

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Key Concepts

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

equation solving
Equation solving is a fundamental skill in basic algebra. It involves finding the value of an unknown variable that makes a given equation true. In the original problem, we started with the equation: \[ n + 268 = 124 \], The goal was to find the value of the variable \( n \). Equation solving typically involves several steps:
  • Understanding the given equation and what it represents. For example, in our question, when 268 is added to the unknown variable \( n \), the result is 124.
  • Using algebraic operations to isolate the variable and solve for its value. This may involve addition, subtraction, multiplication, or division, as we'll elaborate on in the next sections.
  • Lastly, verifying the solution by plugging the value back into the original equation (if necessary) to ensure it satisfies the equation.
isolation of variable
Isolation of the variable involves rearranging an equation so that the unknown variable is by itself on one side of the equation. In the original exercise, we isolated the variable \( n \) by performing the inverse operation of addition.Starting from the equation: \[ n + 268 = 124 \] our goal was to isolate \( n \). To do this, we subtracted 268 from both sides of the equation:
  • Step 1: \[ n + 268 = 124 \]
  • Step 2: Subtract 268 from both sides: \[ n + 268 - 268 = 124 - 268 \]
  • Step 3: Simplify both sides: \[ n = -144 \]
This process left us with \( n \) on one side and its value on the other side. Isolation of variables helps us in solving for the unknown in a clear and systematic way.
basic algebra operations
Basic algebra operations include addition, subtraction, multiplication, and division. They are vital for solving equations and isolating variables. Here's how these operations played a role in solving the original problem.Initially, we had to use subtraction to isolate \( n \):
  • Addition was in the original equation: \[ n + 268 = 124 \]
  • Using subtraction to remove 268:\[ 124 - 268 \]
  • This resulted in: \[ n = -144 \]
Once we determined that \( n = -144 \), we used subtraction again to solve for \( n - 268 \):
  • Substitute \( n \): \[ -144 - 268 \]
  • Subtract to find the result: \[ -412 \]
Basic algebra operations make it possible to manipulate equations and isolate variables, which are essential techniques in algebra.

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