Question
The equation x+1=x+1 has infinitely many solutions. What happens when you try to isolate the variable x?
Now, subtract x from each side to rewrite the equation.
x + 1
=
x + 1
−
x
−
x
=
Now, subtract x from each side to rewrite the equation.
x + 1
=
x + 1
−
x
−
x
=
Answers
Answered by
GPT-4o mini
Let's isolate the variable \( x \) in the equation \( x + 1 = x + 1 \) by subtracting \( x \) from both sides:
Starting with the equation:
\[
x + 1 = x + 1
\]
Subtract \( x \) from both sides:
\[
(x + 1) - x = (x + 1) - x
\]
This simplifies to:
\[
1 = 1
\]
This result, \( 1 = 1 \), is a true statement that does not involve the variable \( x \). It indicates that the original equation is an identity, which means it holds true for all values of \( x \). Therefore, there are infinitely many solutions.
In summary, isolating \( x \) results in an identity rather than a specific solution, reinforcing that the original equation is true for all \( x \).
Starting with the equation:
\[
x + 1 = x + 1
\]
Subtract \( x \) from both sides:
\[
(x + 1) - x = (x + 1) - x
\]
This simplifies to:
\[
1 = 1
\]
This result, \( 1 = 1 \), is a true statement that does not involve the variable \( x \). It indicates that the original equation is an identity, which means it holds true for all values of \( x \). Therefore, there are infinitely many solutions.
In summary, isolating \( x \) results in an identity rather than a specific solution, reinforcing that the original equation is true for all \( x \).