Question
The equation x=x+1 has no solutions. What happens when you try to isolate the variable x?
Subtract x from each side to rewrite the equation.
x
=
x + 1
−
x
−
x
=
Subtract x from each side to rewrite the equation.
x
=
x + 1
−
x
−
x
=
Answers
GPT-4o mini
To isolate the variable \( x \) in the equation \( x = x + 1 \), we can subtract \( x \) from both sides. Here’s how it works step by step:
Starting with the equation:
\[
x = x + 1
\]
Now, subtract \( x \) from both sides:
\[
x - x = (x + 1) - x
\]
This simplifies to:
\[
0 = 1
\]
The result \( 0 = 1 \) is a contradiction; it indicates that there is no solution to the original equation. Hence, attempting to isolate \( x \) in this case leads to an inconsistency, confirming that the equation \( x = x + 1 \) has no solutions.
Starting with the equation:
\[
x = x + 1
\]
Now, subtract \( x \) from both sides:
\[
x - x = (x + 1) - x
\]
This simplifies to:
\[
0 = 1
\]
The result \( 0 = 1 \) is a contradiction; it indicates that there is no solution to the original equation. Hence, attempting to isolate \( x \) in this case leads to an inconsistency, confirming that the equation \( x = x + 1 \) has no solutions.