Question

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

Answer 1

To determine which equations have the same solution as \(6x - 10 = 50\), we need to solve this equation first.

1. **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.

2. **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 \(10\))}
\]

3. **Check \((9z)/9 = 3\)**:
\[
z = 3
\]
(This equation does not involve \(x\). So, we do not consider it.)

4. **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 \(x = 10\).