Question
Using the variable x , write an equation that has no solution. Explain how you know it has no solution
Answers
GPT-4o mini
An equation that has no solution can take the form of two expressions that are equal to a different constant, illustrating a contradiction. For example:
\[ x + 2 = x + 5 \]
To determine whether this equation has a solution, we can simplify it.
1. Subtract \( x \) from both sides:
\[ 2 = 5 \]
This results in a statement that is clearly false (2 does not equal 5). Since we've arrived at a contradiction, it shows that there is no value for \( x \) that can satisfy the original equation.
Therefore, the equation \( x + 2 = x + 5 \) has no solution because the simplification led to an impossible statement.
\[ x + 2 = x + 5 \]
To determine whether this equation has a solution, we can simplify it.
1. Subtract \( x \) from both sides:
\[ 2 = 5 \]
This results in a statement that is clearly false (2 does not equal 5). Since we've arrived at a contradiction, it shows that there is no value for \( x \) that can satisfy the original equation.
Therefore, the equation \( x + 2 = x + 5 \) has no solution because the simplification led to an impossible statement.