Activities

1. Solve the following equations and identify if there is one solution, no solution, or infinite solutions.
   
   
   1. 2x + 12 = 2(-4 + x)
   2. x + 3 + 2x – 9 = 3(x – 2)
   3. -3(a + 4) – 2 = 4a + 10 – a

2. Write a linear equation in one variable that has each of the following.  Verify that your equations satisfy each situation by solving them.
   
   
   1. One solution
   2. No solutions
   3. Infinite solutions

3. Complete each equation so that it has the indicated number of solutions.  Explain how you chose your answer.
   
   
   1. No solutions:  5(x – 2) = 5x – ___
   2. Infinite solutions:  4x – ___ = 2(2x – 1) – 3

4. When you simplify an equation using the properties of equality, you will get one of three results as shown in the table below.  Complete the table explaining what each result means and how many solutions it results in.

Answer Key/Rubric

1. Answers as follows:
   
   
   1. No solution
   2. Infinite solutions
   3. One solution

2. Answers will vary.
   Acceptable answers may include, but are not limited to:

1. One solution – answers must result in x = a
2. No solutions – answers must result in a = b
3. Infinite solutions – answers must result in a = a

3. Acceptable answers may include, but are not limited to:
   
   
   1. Any number is acceptable, except 10.
      No have no solution, the equation must result in a = b.  Since the 5x’s will cancel each other out, any number other than 10 will result in a = b.

2. 5
   In order to have an infinite number of solutions, both sides of the equation must be exactly the same to result in a = a.  Simplifying the left side of the equation will result in 4x – 5, so the missing piece on the right is the 5.

4. Acceptable answers may include, but are not limited to: