Question
All of the following are equivalent except _____.
x - (-2)
x - 2
-2 + x
x + (-2)
x - (-2)
x - 2
-2 + x
x + (-2)
Answers
GPT-4o mini
To determine which of the given expressions is not equivalent to the others, let's simplify each expression:
1. **x - (-2)** = x + 2
2. **x - 2** = x - 2
3. **-2 + x** = x - 2 (since addition is commutative)
4. **x + (-2)** = x - 2
Now, let's rewrite the equivalent forms for clarity:
- **x - (-2)** simplifies to **x + 2**
- **x - 2** is **x - 2**
- **-2 + x** simplifies to **x - 2**
- **x + (-2)** simplifies to **x - 2**
From this analysis, we can see that **x - (-2)** (or **x + 2**) is the only expression that is not equivalent to the others, which all simplify to **x - 2**.
Thus, the answer is: **x - (-2)**.
1. **x - (-2)** = x + 2
2. **x - 2** = x - 2
3. **-2 + x** = x - 2 (since addition is commutative)
4. **x + (-2)** = x - 2
Now, let's rewrite the equivalent forms for clarity:
- **x - (-2)** simplifies to **x + 2**
- **x - 2** is **x - 2**
- **-2 + x** simplifies to **x - 2**
- **x + (-2)** simplifies to **x - 2**
From this analysis, we can see that **x - (-2)** (or **x + 2**) is the only expression that is not equivalent to the others, which all simplify to **x - 2**.
Thus, the answer is: **x - (-2)**.