Question

Use drag and drop to place the two equations below that have the same solution.(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Response area has the same solution as Response area .

the answers are

2 (5x+4) = 8x + 28

x/2 + 4 = 5x - 10

6x - 10 = 50

5x / 9 = 3

Answer 1

To determine which two equations have the same solution, we can solve each equation and compare the solutions.

Let's analyze each equation:

1. **Equation 1: \(2(5x + 4) = 8x + 28\)**
- Distributing on the left side:
\[10x + 8 = 8x + 28\]
- Subtracting \(8x\) from both sides:
\[2x + 8 = 28\]
- Subtracting 8 from both sides:
\[2x = 20\]
- Dividing by 2:
\[x = 10\]

2. **Equation 2: \(\frac{x}{2} + 4 = 5x - 10\)**
- Multiplying the entire equation by 2 to eliminate the fraction:
\[x + 8 = 10x - 20\]
- Subtracting \(x\) from both sides:
\[8 = 9x - 20\]
- Adding 20 to both sides:
\[28 = 9x\]
- Dividing by 9:
\[x = \frac{28}{9}\]

3. **Equation 3: \(6x - 10 = 50\)**
- Adding 10 to both sides:
\[6x = 60\]
- Dividing by 6:
\[x = 10\]

4. **Equation 4: \(\frac{5x}{9} = 3\)**
- Multiplying both sides by 9:
\[5x = 27\]
- Dividing by 5:
\[x = \frac{27}{5}\]

From the analysis:
- Equation 1 has solution \(x = 10\).
- Equation 2 has solution \(x = \frac{28}{9}\).
- Equation 3 has solution \(x = 10\).
- Equation 4 has solution \(x = \frac{27}{5}\).

The two equations that have the same solution are:
- **2(5x + 4) = 8x + 28**
- **6x - 10 = 50**

So, you would drag:
- **2(5x + 4) = 8x + 28** to one response area
- **6x - 10 = 50** to the other response area.