Question
Select how many solutions each equation or inequality has:(3 points)
One solution More than one solution No solution
x>1
y+5=2y
3z−7=3z+7
One solution More than one solution No solution
x>1
y+5=2y
3z−7=3z+7
Answers
GPT-4o mini
Let's analyze each equation or inequality to determine the number of solutions:
1. **\( x > 1 \)**: This inequality has more than one solution because any number greater than 1 (e.g., 1.1, 2, 3, etc.) is a valid solution.
**Answer: More than one solution**
2. **\( y + 5 = 2y \)**: Rearranging this equation gives us \( 5 = 2y - y \) or \( y = 5 \). This equation has exactly one solution.
**Answer: One solution**
3. **\( 3z - 7 = 3z + 7 \)**: If we simplify this equation, we subtract \( 3z \) from both sides, resulting in \( -7 = 7 \), which is a contradiction. This means that there are no solutions.
**Answer: No solution**
### Summary:
- \( x > 1 \): More than one solution
- \( y + 5 = 2y \): One solution
- \( 3z - 7 = 3z + 7 \): No solution
1. **\( x > 1 \)**: This inequality has more than one solution because any number greater than 1 (e.g., 1.1, 2, 3, etc.) is a valid solution.
**Answer: More than one solution**
2. **\( y + 5 = 2y \)**: Rearranging this equation gives us \( 5 = 2y - y \) or \( y = 5 \). This equation has exactly one solution.
**Answer: One solution**
3. **\( 3z - 7 = 3z + 7 \)**: If we simplify this equation, we subtract \( 3z \) from both sides, resulting in \( -7 = 7 \), which is a contradiction. This means that there are no solutions.
**Answer: No solution**
### Summary:
- \( x > 1 \): More than one solution
- \( y + 5 = 2y \): One solution
- \( 3z - 7 = 3z + 7 \): No solution