Question
If \( 12=x+5 \), then \( x+5=12 \) Symmetric Property of Equality Addition Property of Equality Reflexive Property of Equality Subtraction Property of Equality
Ask by Ingram Hanson. in the United States
Jan 24,2025
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Tutor-Verified Answer
Answer
The step \( 12 = x + 5 \) becomes \( x + 5 = 12 \) using the **Symmetric Property of Equality**.
Solution
The step from \( 12 = x + 5 \) to \( x + 5 = 12 \) is justified by the **Symmetric Property of Equality**.
**Symmetric Property of Equality** states that if one quantity equals another, then the second quantity equals the first. In other words, if \( a = b \), then \( b = a \).
**Explanation of Other Properties:**
- **Addition Property of Equality:** Allows you to add the same number to both sides of an equation. For example, if \( a = b \), then \( a + c = b + c \).
- **Subtraction Property of Equality:** Allows you to subtract the same number from both sides of an equation. For example, if \( a = b \), then \( a - c = b - c \).
- **Reflexive Property of Equality:** States that any quantity is equal to itself. For example, \( a = a \).
**Correct Property:**
- **Symmetric Property of Equality**
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Simplify this solution The Deep Dive
Did you know that the Symmetric Property of Equality states that if one quantity equals another, then you can swap them? So, if \( 12 = x + 5 \), it naturally follows that \( x + 5 = 12 \). It’s a simple flip, like magic in algebra! When solving equations, it's easy to make mistakes. One common pitfall is forgetting to keep an equation balanced when performing operations. Always remember: whatever you do to one side of the equation, you must do to the other! This ensures that the equality remains true—a key to avoiding those pesky errors!
