Let's analyze both equations to determine the number of solutions.
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For the equation \( x = x + 7 \):
- We can rearrange it to: \( x - x = 7 \), which simplifies to \( 0 = 7 \).
- This statement is false, meaning there are no solutions to this equation.
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For the equation \( 3(x + 2) = 3x + 6 \):
- Expand the left side: \( 3x + 6 = 3x + 6 \).
- This simplifies to \( 3x + 6 = 3x + 6 \), which is always true.
- Since both sides are equal for any value of \( x \), there are infinite solutions to this equation.
In summary:
- The first equation \( x = x + 7 \) has no solutions.
- The second equation \( 3(x + 2) = 3x + 6 \) has infinite solutions.
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