Write an equation with a variable on both sides of the equal sign that had no solution. Solve the equation and explain why it has no solution.
3x + 5 = 2x + 8
To solve this equation, we need to isolate the variable on one side of the equal sign.
Subtract 2x from both sides:
3x - 2x + 5 = 2x - 2x + 8
x + 5 = 8
Subtract 5 from both sides:
x + 5 - 5 = 8 - 5
x = 3
However, when we plug the solution x = 3 back into the original equation:
3(3) + 5 = 2(3) + 8
9 + 5 = 6 + 8
14 = 14
This shows that both sides of the equation are equal when x = 3, meaning that there is a solution. Therefore, an equation with no solution would be one where after solving the equation, the two sides do not end up being equal.