Final answer:
The given equations, 2x+3x+100=15x+20 and 5x+100=15x+20, have the same solution, x=8, which means they are the same equation.
Step-by-step explanation:
The two equations given are:
2x+3x+100=15x+20
5x+100=15x+20
To determine how these equations are the same and different, we can simplify both equations.
For the first equation, combine like terms:
5x+100=15x+20
Combine the x terms:
5x-15x+100=20
-10x+100=20
Subtract 100 from both sides:
-10x=20-100
-10x=-80
Divide both sides by -10:
x=8
The solution to the first equation is x=8.
For the second equation, combine like terms:
5x+100=15x+20
Combine the x terms:
5x-15x+100=20
-10x+100=20
Subtract 100 from both sides:
-10x=20-100
-10x=-80
Divide both sides by -10:
x=8
The solution to the second equation is x=8.
Therefore, the two equations have the same solution, x=8, which means they are the same equation.