Question

Give an example of a linear equation in one variable with no solution. Explain how you know it has no solution.

Answer 1

2x + 5 = 2x - 13 has no solution.  You can eliminate the 2x terms by subtraction, ending up with 5 = -13 (which is never true).

Answer 2

5x + 2 = 5(x + 1)

Lets try solving this

5x + 2 = 5x + 5

This is  not solvable whatever value you put for x the left side will never be equal to the right side.  So its No solution