Select all of the equivalence properties that are used to simplify the equation below. There may be more than one.
 
x−210=7

10(x−210)=10(7)

x−2=70

x−2+2=70+2

x=72 

Additive

Subtractive

Multiplication

Division

The equation simplifies as follows:

1. **Starting equation**:
   \[
   \frac{x - 2}{10} = 7
   \]

2. **Multiplying both sides by 10**:
   \[
   10 \times \frac{x - 2}{10} = 10 \times 7
   \]
   This results in:
   \[
   x - 2 = 70
   \]
   **Property used**: Multiplication

3. **Adding 2 to both sides**:
   \[
   x - 2 + 2 = 70 + 2
   \]
   This simplifies to:
   \[
   x = 72
   \]
   **Property used**: Additive

### **Selected equivalence properties**:
- **Multiplication**
- **Additive**

Would you like any more details or have any other questions? Here are some related questions:

1. How do you identify the equivalence properties in different types of equations?
2. Can subtraction be considered an equivalence property in certain cases?
3. What is the role of division in simplifying equations like this?
4. How does additive property differ from the subtractive property in equation solving?
5. What are the general steps to solving linear equations?

**Tip:** Always perform the same operation on both sides of an equation to maintain equality.

Select all of the equivalence properties that are used to simplify the equation below. There may be more than one.

x−2/10=7

10(x−2/10)=10(7)

x−2=70

x−2+2=70+2

x=72

Additive

Subtractive

Multiplication

Division

Explore how to simplify the equation x−2/10=7 using multiplication and addition properties of equality. This step-by-step guide is perfect for students in Grades 6-8, focusing on key algebraic concepts.

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