1. The following pairs of equations are equivalent. Describe the operation that occurred in the second equation.
2. Complete the following table with the properties used to solve 4(x+3)=20.
| Statement |
Proof |
| 4 (x+3) = 20 |
Given |
| 4x + 12 = 20 |
|
| 4x = 8 |
|
| x = 2 |
|
3. Complete the following table with the mathematical statements that correspond to the proofs used to solve 
| Statement |
Proof |
| |
Given |
| |
Multiplication Property of Equality |
| |
Distributive Property |
| |
Addition Property of Equality |
| |
Division Property of Equality |
4. Consider the equations 5x + 10 = 30 and 5 (x+10) = 30.
Do they have the same solution? Why or why not?
5. Consider the equations 3x + 2 = 14 and 2+3x = 14.
Do they have the same solution? Why or why not?
6. Consider the equation 3 (x+2)+3x = 36
Without solving. Name all the properties that would be used to solve the equation.
7. Consider the equation
Part A: Write an equivalent equation using the multiplication property of equality.
Part B: What properties will you use next to solve the equation?
8. Solve the following equation. Justify each step.
0.2x + 3.1 - 2.1x = 0.3 (x-5) + 0.2
