Question
Does x - 7 = 7 - x
Have infinite solutions, none, one, or two?
Have infinite solutions, none, one, or two?
Answers
GPT-4o mini
To solve the equation \( x - 7 = 7 - x \), we can start by rearranging the equation to combine like terms.
1. Add \( x \) to both sides:
\[
x + x - 7 = 7
\]
This simplifies to:
\[
2x - 7 = 7
\]
2. Next, add 7 to both sides:
\[
2x = 7 + 7
\]
This simplifies to:
\[
2x = 14
\]
3. Now divide both sides by 2:
\[
x = 7
\]
So, the equation \( x - 7 = 7 - x \) has one solution, which is \( x = 7 \).
Thus, the answer is **one solution**.
1. Add \( x \) to both sides:
\[
x + x - 7 = 7
\]
This simplifies to:
\[
2x - 7 = 7
\]
2. Next, add 7 to both sides:
\[
2x = 7 + 7
\]
This simplifies to:
\[
2x = 14
\]
3. Now divide both sides by 2:
\[
x = 7
\]
So, the equation \( x - 7 = 7 - x \) has one solution, which is \( x = 7 \).
Thus, the answer is **one solution**.