To determine which of the equations have the same solution, we can solve each equation.
-
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 \(2\): \(x = 10\)
-
Equation: \(\frac{5x}{9} = 3\)
- Multiply both sides by \(9\): \(5x = 27\)
- Divide by \(5\): \(x = \frac{27}{5}\)
-
Equation: \(6x - 10 = 50\)
- Add \(10\) to both sides: \(6x = 60\)
- Divide by \(6\): \(x = 10\)
-
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:
- \(2(5x + 4) = 8x + 28\)
- \(6x - 10 = 50\)
1 answer