Question

Match the description of the one variable equation with the number of solutions it will have.(4 points)
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x−7=7−x
3(x+5)=3x+5
10−x=25
2(x+4)=2x+5+3

Answer 1

To match the descriptions of the one variable equations with the number of solutions, let's analyze each equation:

1. **Equation: x − 7 = 7 − x**

This simplifies to:
- x + x = 7 + 7
- 2x = 14
- x = 7

**Number of solutions: 1 (one solution)**

2. **Equation: 3(x + 5) = 3x + 5**

This simplifies to:
- 3x + 15 = 3x + 5
- 15 = 5 (which is false)

**Number of solutions: 0 (no solution)**

3. **Equation: 10 − x = 25**

This simplifies to:
- -x = 25 - 10
- -x = 15
- x = -15

**Number of solutions: 1 (one solution)**

4. **Equation: 2(x + 4) = 2x + 5 + 3**

This simplifies to:
- 2x + 8 = 2x + 8
- 8 = 8 (which is always true)

**Number of solutions: Infinite (infinitely many solutions)**

Now, let's summarize the matches:

- **x − 7 = 7 − x**: 1 solution
- **3(x + 5) = 3x + 5**: 0 solutions
- **10 − x = 25**: 1 solution
- **2(x + 4) = 2x + 5 + 3**: Infinite solutions

This gives us the matching descriptions.