Question
Identify the properties for each step used to solve the equation: 5 - 3 (x + 3) = 11 - 8x
Step 1: 5x = 15
Step 2: 5 - 3x - 9 = 11 - 8x
Step 3: x = 3
Step 4: 5x - 4 = 11
Step 5: -3x - 4 = 11 - 8x
Options: Subtraction Property of Equalities, Multiplication Property of Equalities, Division Property of Equalities, Combine Like Terms, Distributive Property, Addition Property of Equalities
Step 1: 5x = 15
Step 2: 5 - 3x - 9 = 11 - 8x
Step 3: x = 3
Step 4: 5x - 4 = 11
Step 5: -3x - 4 = 11 - 8x
Options: Subtraction Property of Equalities, Multiplication Property of Equalities, Division Property of Equalities, Combine Like Terms, Distributive Property, Addition Property of Equalities
Answers
GPT-4o mini
Let's identify the properties used in each step of solving the equation \( 5 - 3(x + 3) = 11 - 8x \):
### Step 1: 5x = 15
This step seems to be leading to a conclusion based on earlier steps. We need to check the preceding calculations to understand how it got to \( 5x = 15 \).
### Step 2: 5 - 3x - 9 = 11 - 8x
In this step, we have applied the **Distributive Property** to remove the parentheses in \( -3(x + 3) \) and combined the constant terms \( 5 - 9 \).
### Step 3: x = 3
In this step, we simplify the equation to isolate \( x \). The property at play here is likely the **Division Property of Equalities**, assuming we divided both sides of the equation by a common factor for simplification.
### Step 4: 5x - 4 = 11
This step appears to be a reorganization or simplification of the prior step. The property is likely the **Addition Property of Equalities** if we moved terms from one side to another, but also might involve combining like terms.
### Step 5: -3x - 4 = 11 - 8x
In this step, it looks like terms have been moved or rearranged, which again brings us to the **Subtraction Property of Equalities** if we subtracted from both sides or **Combine Like Terms** if we are combining or simplifying further.
In summary:
- **Step 2:** Distributive Property
- **Step 3:** Division Property of Equalities
- **Step 4:** Likely Addition Property of Equalities / Combine Like Terms
- **Step 5:** Likely Subtraction Property of Equalities / Combine Like Terms
Therefore, more context on steps leading to or ensuring clarity on each would be beneficial for absolute precision in identifying properties directly.
### Step 1: 5x = 15
This step seems to be leading to a conclusion based on earlier steps. We need to check the preceding calculations to understand how it got to \( 5x = 15 \).
### Step 2: 5 - 3x - 9 = 11 - 8x
In this step, we have applied the **Distributive Property** to remove the parentheses in \( -3(x + 3) \) and combined the constant terms \( 5 - 9 \).
### Step 3: x = 3
In this step, we simplify the equation to isolate \( x \). The property at play here is likely the **Division Property of Equalities**, assuming we divided both sides of the equation by a common factor for simplification.
### Step 4: 5x - 4 = 11
This step appears to be a reorganization or simplification of the prior step. The property is likely the **Addition Property of Equalities** if we moved terms from one side to another, but also might involve combining like terms.
### Step 5: -3x - 4 = 11 - 8x
In this step, it looks like terms have been moved or rearranged, which again brings us to the **Subtraction Property of Equalities** if we subtracted from both sides or **Combine Like Terms** if we are combining or simplifying further.
In summary:
- **Step 2:** Distributive Property
- **Step 3:** Division Property of Equalities
- **Step 4:** Likely Addition Property of Equalities / Combine Like Terms
- **Step 5:** Likely Subtraction Property of Equalities / Combine Like Terms
Therefore, more context on steps leading to or ensuring clarity on each would be beneficial for absolute precision in identifying properties directly.