literal equation

Question

1. Create a single variable linear equation that has no solution. Solve the equation algebraically to prove that it does not have a solution.
2. Create a single variable linear equation that has one solution. Solve the equation algebraically to prove that there is one distinct solution for the equation.
3. Create a single variable linear equation that has infinitely many solutions. Solve the equation algebraically to prove that there is an infinite number of solutions for the equation

Answer 1

2x = 2x + 1

subtract 2x from both sides to get

0 = 1 which is always untrue regardless of the value of x. the equation has no solution

2x= x + 1

subtract x from both sides to get

x = 1, which is one unique solution

The

x + 1 = x + 1

subtract x from both sides

1=1 which is always true for all values of x. The equation has an infinite number of solutions.