To determine which equations have the same solution as \(6x - 10 = 50\), we need to solve this equation first.
- Solve \(6x - 10 = 50\): \[ 6x - 10 = 50 \] Add 10 to both sides: \[ 6x = 60 \] Divide both sides by 6: \[ x = 10 \]
Now we will check the other equations to see if they also have \(x = 10\) as their solution.
-
Check \(x/2 + 4 = 5x - 10\): \[ \frac{x}{2} + 4 = 5x - 10 \] Multiply through by 2 to eliminate the fraction: \[ x + 8 = 10x - 20 \] Rearranging gives: \[ 8 + 20 = 10x - x \] \[ 28 = 9x \] \[ x = \frac{28}{9} \text{ (not equal to \(10\))} \]
-
Check \((9z)/9 = 3\): \[ z = 3 \] (This equation does not involve \(x\). So, we do not consider it.)
-
Check \(2(5x + 4) = 8x + 28\): \[ 2(5x + 4) = 8x + 28 \] Expanding the left side: \[ 10x + 8 = 8x + 28 \] Rearranging gives: \[ 10x - 8x = 28 - 8 \] \[ 2x = 20 \] \[ x = 10 \]
Now, we found that:
- \(x/2 + 4 = 5x - 10\) does not have the same solution as \(6x - 10 = 50\).
- \((9z)/9 = 3\) is irrelevant.
- \(2(5x + 4) = 8x + 28\) has the same solution as \(6x - 10 = 50\).
Thus, the equations with the same solution as \(6x - 10 = 50\) are:
- \(2(5x + 4) = 8x + 28\)
Please drag and drop:
- \(6x - 10 = 50\)
- \(2(5x + 4) = 8x + 28\)
Both share the same solution \(x = 10\).
1 answer