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

Answer:

1. a single variable linear equation that has no solution

x + 4 = x + 5

x - x = 5 - 4

0 = 1 (which is false)

2. a single variable linear equation that has one solution

2x + 4 = x + 5

2x  - x = 5 - 4

x = 1

3. a single variable linear equation that has infinitely many solutions

x + 4 - 1= x + 3 

x - x = 3 - 4 + 1

0 = 0 (identity)