Use drag and drop to place the two equations below that have the same solution.(1 point)

Question

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.
____ has the same solution as _______ .
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 will solve each equation step by step:

1. Equation: \(2(5x+4)=8x+28\)

   Simplifying: \[ 10x + 8 = 8x + 28 \] Subtract \(8x\) from both sides: \[ 2x + 8 = 28 \] Subtract \(8\) from both sides: \[ 2x = 20 \] Divide by \(2\): \[ x = 10 \]

2. Equation: \(\frac{x}{2}+4=5x-10\)

   Simplifying: \[ \frac{x}{2} + 4 = 5x - 10 \] Multiply through by \(2\) to eliminate the fraction: \[ x + 8 = 10x - 20 \] Subtract \(x\) from both sides: \[ 8 = 9x - 20 \] Add \(20\) to both sides: \[ 28 = 9x \] Divide by \(9\): \[ x = \frac{28}{9} \]

3. Equation: \(6x - 10 = 50\)

   Simplifying: \[ 6x = 60 \] Divide by \(6\): \[ x = 10 \]

4. Equation: \(\frac{5x}{9}=3\)

   Simplifying: \[ 5x = 27 \] Divide by \(5\): \[ x = \frac{27}{5} \]

Summary of Solutions:

• First Equation: \(x = 10\)
• Second Equation: \(x = \frac{28}{9}\)
• Third Equation: \(x = 10\)
• Fourth Equation: \(x = \frac{27}{5}\)

Conclusion:

The equations that have the same solution are:

2(5x+4)=8x+28 has the same solution as 6x - 10 = 50.

So the final answer is:

2(5x+4)=8x+28 has the same solution as 6x - 10 = 50.