Question

Use drag and drop to place the two equations below that have the same solution.(1 point)
Response area has the same solution as
2(5x+4)=8x+28
5x/9 =3
6x-10=50
x/2 +4=5x-10

Answer 1

To determine which of the equations have the same solution, we can solve each equation.

1. **Equation: \(2(5x + 4) = 8x + 28\)**
- Distribute: \(10x + 8 = 8x + 28\)
- Subtract \(8x\) from both sides: \(2x + 8 = 28\)
- Subtract \(8\) from both sides: \(2x = 20\)
- Divide by \(2\): \(x = 10\)

2. **Equation: \(\frac{5x}{9} = 3\)**
- Multiply both sides by \(9\): \(5x = 27\)
- Divide by \(5\): \(x = \frac{27}{5}\)

3. **Equation: \(6x - 10 = 50\)**
- Add \(10\) to both sides: \(6x = 60\)
- Divide by \(6\): \(x = 10\)

4. **Equation: \(\frac{x}{2} + 4 = 5x - 10\)**
- Subtract \(4\) from both sides: \(\frac{x}{2} = 5x - 14\)
- Multiply both sides by \(2\): \(x = 10x - 28\)
- Subtract \(10x\) from both sides: \(-9x = -28\)
- Divide by \(-9\): \(x = \frac{28}{9}\)

### Solutions Summary:
- \(2(5x + 4) = 8x + 28\) -> \(x = 10\)
- \(\frac{5x}{9} = 3\) -> \(x = \frac{27}{5}\)
- \(6x - 10 = 50\) -> \(x = 10\)
- \(\frac{x}{2} + 4 = 5x - 10\) -> \(x = \frac{28}{9}\)

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

So the correct drag-and-drop placement for the response area is:
- **has the same solution as**:
- \(2(5x + 4) = 8x + 28\)
- \(6x - 10 = 50\)