1. Start with the first equation: 3x + 18 = 5x + 8
2. Subtract 3x from both sides: 18 = 2x + 8.
3. Subtract 8 from both sides: 10 = 2x.
4. Divide by 2: x = 5
5. Substitute x back into the equation to check: 3(5) + 18 = 5(5) + 8
15 + 18 = 25 + 8
33 = 33
So x = 5 is a valid solution for the first equation.
6. Move on to the second equation: 4x + 22 = 8x + 10
7. Subtract 4x from both sides: 22 = 4x + 10
8. Subtract 10 from both sides: 12 = 4x
9. Divide by 4: x = 3
10. Substitute x back into the equation to check: 4(3) + 22 = 8(3) + 10
12 + 22 = 24 + 10
34 = 34
So x = 3 is a valid solution for the second equation.
Since x = 5 is the solution for the first equation and x = 3 is the solution for the second equation, these two equations have different unique solutions, which makes it clear that there is only one solution in each equation.