Problem 82 Solve. $$ x+2=x+3 $$... [FREE SOLUTION]

91影视

Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger, David J. Ellenbogen, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

10 Edition

Chapter 1: Problem 82

Solve. $$ x+2=x+3 $$

Short Answer

Expert verified

No solution (contradiction)

Step by step solution

- Write down the equation

Start with the given equation: $ x + 2 = x + 3 $

- Subtract x from both sides

Subtract $ x $ from both sides to eliminate the variable from one side: $ x + 2 - x = x + 3 - x $

- Simplify both sides

Simplify both sides of the equation: $ 2 = 3 $

- Analyze the result

The resulting statement $ 2 = 3 $ is a contradiction, which means there is no value of $ x $ that will satisfy the original equation.

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Key Concepts

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

Equation Contradiction

Sometimes, while solving linear equations, you may end up with a result that seems completely illogical. For example, in the given equation: $x + 2 = x + 3$, after removing the variable, you end up with $2 = 3$. This is known as a contradiction. The left side and the right side of the equation cannot be equal. Contradictions usually indicate that the original equation has been manipulated incorrectly, or there is no solution for the variable involved. They are essential in helping us understand limitations within the algebraic manipulations.

No Solution

Let's look more closely at the idea of a 'no solution' scenario. In our equation: $x + 2 = x + 3$, after subtracting $x$ from both sides, the resulting $2 = 3$ is clearly false. This means there is no value of $x$ that can make the original equation true. When you see a false statement like this, we've reached what is known as an 'inconsistent equation', indicating there is no solution. Not all equations have a solution, and understanding this helps to refine your problem-solving skills in algebra.

Basic Algebra Manipulation

Basic algebraic manipulation is key to solving equations. Here are the typical steps used for our problem:

Start with the given equation: $x + 2 = x + 3$.
To isolate the variables, subtract $x$ from both sides to simplify: $ x + 2 - x = x + 3 - x $.
After simplification, you get $ 2 = 3 $.
Always follow these basic principles:

Perform the same operations on both sides of the equation.
Simplify each step for clearer understanding.
Analyze the final result 鈥� if it鈥檚 a true statement, you found your solution. If false, there鈥檚 no solution.

These steps are foundational and help systematically tackle algebra problems.

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91影视

Solve. $$ x+2=x+3 $$

Short Answer

Step by step solution

- Write down the equation

- Subtract x from both sides

- Simplify both sides

- Analyze the result

Key Concepts

Equation Contradiction

No Solution

Basic Algebra Manipulation

One App. One Place for Learning.

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