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