To solve the equation [tex]\( 7y - 15 = -29 \)[/tex], we can use the following properties:
1. Addition Property of Equality: This property states that if you add the same number to both sides of an equation, the equality is maintained. This can be used to isolate the term containing the variable [tex]\( y \)[/tex].
2. Inverse Property of Multiplication: This property states that if you multiply a number by its multiplicative inverse (or divide by the number), you get 1. This can be used to solve for [tex]\( y \)[/tex] once it has been isolated.
Let's break down the steps to solve [tex]\( 7y - 15 = -29 \)[/tex] using these properties:
### Step-by-Step Solution:
#### Step 1: Apply the Addition Property of Equality
We want to isolate the term involving [tex]\( y \)[/tex]. To do this, we need to eliminate the constant term [tex]\(-15\)[/tex] on the left-hand side.
Add [tex]\( 15 \)[/tex] to both sides:
[tex]\[ 7y - 15 + 15 = -29 + 15 \][/tex]
This simplifies to:
[tex]\[ 7y = -14 \][/tex]
#### Step 2: Apply the Inverse Property of Multiplication
Now, we need to solve for [tex]\( y \)[/tex]. The term [tex]\( 7y \)[/tex] means [tex]\( y \)[/tex] is being multiplied by [tex]\( 7 \)[/tex]. To isolate [tex]\( y \)[/tex], we can divide both sides of the equation by [tex]\( 7 \)[/tex] (which is the same as multiplying by the inverse of [tex]\( 7 \)[/tex]):
[tex]\[ y = \frac{-14}{7} \][/tex]
This simplifies to:
[tex]\[ y = -2 \][/tex]
### Conclusion:
The properties used to solve the equation [tex]\( 7y - 15 = -29 \)[/tex] are the Addition Property of Equality and the Inverse Property of Multiplication.
Therefore, the correct answers are:
- Addition Property of Equality
- Inverse Property of Multiplication
