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Chapter 1: Problem 68

Find a solution for each equation. $$n+4=7$$

Short Answer

Expert verified
The solution to the equation is \( n = 3 \).

Step by step solution

01

Identify the Equation

We have the equation \( n + 4 = 7 \). Our goal is to find the value of \( n \) that makes this equation true.
02

Isolate the Variable

To isolate \( n \), we need to get rid of the constant added to it. We do this by subtracting 4 from both sides of the equation.
03

Perform the Subtraction

Subtract 4 from both sides: \( n + 4 - 4 = 7 - 4 \).
04

Simplify Both Sides

Simplify both sides of the equation: \( n = 3 \).

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Key Concepts

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

Prealgebra
Prealgebra is a foundational mathematics course that sets the stage for algebra. It introduces students to basic algebraic concepts using simple arithmetic.Prealgebra focuses on understanding variables, expressions, and simple equations. Let's dive deeper:
  • **Variables**: Letters like \( n \) represent unknown values.
  • **Expressions**: Combinations of numbers and variables, like \( n + 4 \).
  • **Equations**: Mathematical statements showing equality, e.g., \( n + 4 = 7 \).
These basic concepts allow students to ease into the more advanced studies of algebra. Prealgebra uses familiar ideas like addition, subtraction, and equal signs to build new skills.
Basic Arithmetic Operations
Basic arithmetic operations such as addition, subtraction, multiplication, and division are crucial in solving equations.To solve the equation \( n + 4 = 7 \), we must understand:
  • **Addition**: Combining two numbers to get a sum.
  • **Subtraction**: Finding the difference between numbers by taking one away from another.
In our example, subtraction is used to simplify the equation. We subtract 4 from both sides, effectively removing the constant term.This operation balances the equation, leaving the variable \( n \) by itself. It's like balancing both sides of a scale.
Isolation of Variables
Isolation of variables involves manipulating an equation to get the variable alone on one side. This makes it easy to see the solution.Consider the equation \( n + 4 = 7 \). We isolate \( n \) by removing 4:
  • **Subtract 4**: Doing this on both sides keeps the equation balanced, just like keeping a seesaw level.
  • **Result**: This gives us \( n = 3 \), as both sides simplify to equal numbers.
Isolation of the variable is key to solving equations. It lets us find the specific value that makes the original equation true. Through practice, such skills become second nature in algebra.

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Most popular questions from this chapter

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