To determine which two equations have the same solution, we'll solve each equation one by one.
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Equation 1: \( \frac{5x}{9} = 3 \)
Multiply both sides by 9: \[ 5x = 27 \] Divide both sides by 5: \[ x = \frac{27}{5} = 5.4 \]
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Equation 2: \( 2(5x + 4) = 8x + 28 \)
Distribute the 2: \[ 10x + 8 = 8x + 28 \] Subtract \(8x\) from both sides: \[ 2x + 8 = 28 \] Subtract 8 from both sides: \[ 2x = 20 \] Divide by 2: \[ x = 10 \]
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Equation 3: \( 6x - 10 = 50 \)
Add 10 to both sides: \[ 6x = 60 \] Divide by 6: \[ x = 10 \]
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Equation 4: \( \frac{x}{2} + 4 = 5x - 10 \)
Multiply everything 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: \[ x = \frac{28}{9} \approx 3.11 \]
Now, let's summarize the solutions:
- From Equation 1: \(x = \frac{27}{5} = 5.4\)
- From Equation 2: \(x = 10\)
- From Equation 3: \(x = 10\)
- From Equation 4: \(x = \frac{28}{9} \approx 3.11\)
The equations that have the same solution are Equation 2 and Equation 3, both yielding \(x = 10\).