Question

x= x + 7 has
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3(x + 2) = 3x + 6 has
Previous
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choose your answer...
one solution
no solution
infinite solutions

Answer 1

Let's analyze both equations to determine the number of solutions.

1. **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.

2. **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**.