Question

Order the steps for solving the equation: 2x - 5 = 3(4x + 5)
Step 1: _________ Property to get __________
Step 2: ________ Property to get _______
Step 3: __________ Property to get ____
Step 4: _________ Property to get ____
Fill in the blanks
Part 1 (part 1)
A. Addition of Equality
B. Division of Equality
C. Combine Like Terms
D. Distributive
E. Subtraction of Equality
Part 1 (part 2)
A. 2x - 5 = 12x + 5
B. 2x = 12x + 10
C. 2x = 12x
D. 2x - 5 = 12x + 15
Part 2 (part 1)
A. Distributive
B. Combine Like Terms
C. Division of Equality
D. Addition of Equality
Part 2 (part 2)
A. 2x = 12x + 20
B. 2x = 12x + 10
C. 2x = 3x + 10
D. 2x = 3x + 20
Part 3 (part 1)
A. Subtraction of Equality
B. Combine Like Terms
C. Division of Equality
D. Distributive
Part 3 (part 2)
A. 14x = 20
B. -10x = 20
C. -1x = 10
D. -10x = 10
Part 4 (part 1)
A. Addition of Equality
B. Distributive
C. Combine Like Terms
D. Division of Equality
Part 4 (part 2)
A. x = -3/20
B. x = 1
C. x = -2
D. x = -1/10

Answer 1

To solve the equation \(2x - 5 = 3(4x + 5)\), we can follow these steps:

### Step-by-step Breakdown:

**Step 1:** Apply the **Distributive** Property to get **2x - 5 = 12x + 15**.
- (Part 1: D, Part 2: A)

**Step 2:** Apply the **Addition of Equality** property to get **2x - 12x = 15 + 5**.
- (Part 1: A, Part 2: B)

**Step 3:** Apply the **Combine Like Terms** property to get **-10x = 20**.
- (Part 3: B, Part 3: A)

**Step 4:** Apply the **Division of Equality** property to get **x = -2**.
- (Part 4: D, Part 4: C)

Here’s the full fill-in of the blanks based on the sequential reasoning:

### Final Answer:

**Step 1:** D. Distributive Property to get A. \(2x - 5 = 12x + 15\)
**Step 2:** A. Addition of Equality Property to get B. \(2x - 12x = 15 + 5\)
**Step 3:** B. Combine Like Terms Property to get A. \(-10x = 20\)
**Step 4:** D. Division of Equality Property to get C. \(x = -2\)

Answer 2

are you sure this is correct

Answer 3

I apologize for any mistakes in my previous response. Let's carefully solve the equation step by step to ensure the correctness of the approach.

We start with the equation:

\[ 2x - 5 = 3(4x + 5) \]

### Step 1: Apply the Distributive Property
We distribute the 3 on the right side:

\[ 2x - 5 = 12x + 15 \]
- (Part 1: D, Part 2: A)

### Step 2: Move like terms together
Now we can rearrange to collect like terms. We'll subtract \(12x\) from both sides:

\[ 2x - 12x - 5 = 15 \]
This simplifies to:
\[ -10x - 5 = 15 \]
- However, to focus on what's needed, we can express it directly:
\[ 2x - 12x = 15 + 5 \]
- (Part 1: A, Part 2: B)

### Step 3: Combine Like Terms
Combining like terms gives us:

\[ -10x = 20 \]
- (Part 3: B, Part 3: A)

### Step 4: Divide to solve for \(x\)
Now we divide both sides by -10:

\[ x = -2 \]
- (Part 4: D, Part 4: C)

### Final Fill-in-the-Blanks:

1. **Step 1:** D. Distributive Property to get A. \(2x - 5 = 12x + 15\)
2. **Step 2:** A. Addition of Equality Property to get B. \(2x - 12x = 15 + 5\)
3. **Step 3:** B. Combine Like Terms Property to get A. \(-10x = 20\)
4. **Step 4:** D. Division of Equality Property to get C. \(x = -2\)

Thank you for your patience, and I apologize for the confusion in my initial response.