Question

Determine which expressions are equivalent to the expressions in the table. Place each expression in the appropriate column of the table. Equivalent to 1/2 * x + 10 Equivalent to x - 10

Answer 1

To determine which expressions are equivalent to \( \frac{1}{2}x + 10 \) and \( x - 10 \), we can analyze and manipulate some expressions.

1. **Equivalent to \( \frac{1}{2}x + 10 \)**:
- \( \frac{1}{2}x + 10 \) is already provided.
- Any expression that simplifies to \( \frac{1}{2}x + 10 \) or is mathematically the same.

2. **Equivalent to \( x - 10 \)**:
- \( x - 10 \) is already provided.
- Any expression that simplifies to \( x - 10 \) or is mathematically the same.

Let's look at some possible expressions:

- \( 10 + \frac{1}{2}x \) is equivalent to \( \frac{1}{2}x + 10 \) (order of addition doesn't matter).
- \( \frac{2}{4}x + 10 \) is also equivalent to \( \frac{1}{2}x + 10 \).
- \( 2 \cdot \frac{1}{2}x + 10 \) simplifies to \( \frac{1}{2}x + 10 \) (still equivalent).
- \( x - 10 \cdot 1 \) is equivalent to \( x - 10 \).
- \( x + (-10) \) is also equivalent to \( x - 10 \).
- \( x - 5 - 5 \) is equivalent to \( x - 10 \).

Now we can organize the expressions into the appropriate columns of the table.

**Table:**

| Equivalent to \( \frac{1}{2}x + 10 \) | Equivalent to \( x - 10 \) |
|----------------------------------------|-----------------------------|
| \( 10 + \frac{1}{2}x \) | \( x - 10 \) |
| \( \frac{2}{4}x + 10 \) | \( x + (-10) \) |
| \( 2 \cdot \frac{1}{2}x + 10 \) | \( x - 5 - 5 \) |

If you have specific expressions to check for equivalency, please provide them, and I can help you verify!