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.
1. 3x + 7 = 3x - 9
We can subtract 3x from both sides to get:
7 = -9
This is obviously false, so there is no solution.
2. 2x + 5 = 9
We can subtract 5 from both sides to get:
2x = 4
Then divide both sides by 2:
x = 2
So there is one distinct solution, x = 2.
3. 4x - 8 = 4(x - 2)
If we distribute the 4 on the right-hand side, we get:
4x - 8 = 4x - 8
Notice that we have the exact same expression on both sides. This means that no matter what value of x we plug in, the equation will always be true. Therefore, there are infinitely many solutions.