Create a single variable linear equation that has no solution. Solve the equation algebraically to prove that it does not have a solution.
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.
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
Equation with no solution: 2x + 5 = 2x + 8
This equation can be simplified to 5 = 8, which is a contradiction. Therefore, there is no solution.
Equation with one solution: 4x + 7 = 23
Subtracting 7 from both sides, we get 4x = 16. Dividing both sides by 4, we get x = 4. Therefore, there is one distinct solution, x = 4.
Equation with infinitely many solutions: 3x + 9 = 3(x + 3)
Expanding the right-hand side, we get 3x + 9 = 3x + 9. This is true for all values of x, so there are infinitely many solutions.