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

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.