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PWIFE-581 - To solve the equations and determine the number of solutions for each equation, I'll analyze each equation individually.### 1. 3x + 2 = 3x - 2**Solution:**Let's solve the equation:1. **Subtract 3x from both sides:** ``` 3x + 2 - 3x = 3x - 2 - 3x 2 = -2 ``` 2. **Conclusion:** The equation simplifies to `2 = -2`, which is a contradiction. Therefore, the equation has **no solutions**.**Answer:** **(0)**### 2. 6x + 1 = 6x + 1**Solution:**Let's solve the equation:1. **Subtract 6x from both sides:** ``` 6x + 1 - 6x = 6x + 1 - 6x 1 = 1 ``` 2. **Conclusion:** The equation simplifies to `1 = 1`, which is an identity. Therefore, the equation has **infinitely many solutions**.**Answer:** **(∞)**### 3. 9x - 3 = 9x - 3**Solution:**Let's solve the equation:1. **Subt 9x from both sides:** ``` 9x - 3 - 9x = 9x - 3 - 9x -3 = -3 ``` 2. **Conclusion:** The equation simplifies to `-3 = -3`, which is an identity. Therefore, the equation has **infinitely many solutions**.**Answer:** **(∞)**### 4. 12x + 4 = 12x - 4**Solution:**Let's solve the equation:1. **Subtract 12x from both sides:** ``` 12x + 4 - 12x = 12x - 4 - 12x 4 = -4 ``` 2. **Conclusion:** The equation simplifies to `4 = -4`, which is a contradiction. Therefore, the equation has **no solutions**.**Answer:** **(0)**### 5. 18x - 1 = 7x - 1**Solution:**Let's solve the equation:1. **Subtract 7x from both sides:** ``` 18x - 1 - 7x = 7x - 1 - 7x 11x - 1 = -1 ``` 2. **Add 1 to both sides:** ``` 11x - 1 + 1 = -1 + 1 11x = 0 ``` 3. **Divide by 11:** ``` x = 0 ``` 4. **Conclusion:** The equation has **one solution**.**Answer:** **(1)****Final Answer:**1. **(0)**2. **(∞)**3. **(∞)**4. **(0)**5. **(1)**
2019年9月18日
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