Question

The steps to solve the equation 3 x plus left-parenthesis 10 plus 2 x right-parenthesis equals 0 are shown.



Drag and drop the properties of equality to the table to justify each step.

Response area with 3 blank spaces
Solution Step

Justification

3 x plus left-parenthesis 10 minus 2 x right-parenthesis equals 0
Original equation

3 x plus left-parenthesis negative 2 x plus 10 right-parenthesis equals 0
Blank space 1 empty

left-parenthesis 3 x minus 2 x right-parenthesis plus 10 equals 0
Blank space 2 empty

x plus 10 equals 0
Simplification

x plus 10 plus left-parenthesis negative 10 right-parenthesis equals 0 plus left-parenthesis negative 10 right-parenthesis
Blank space 3 empty

x equals negative 10
Simplification

Answer 1

To complete the justification for each step of the equation \(3x + (10 + 2x) = 0\), here’s how you could fill in the properties of equality:

| Solution Step | Justification |
|------------------------------------------------------------|--------------------------------|
| \(3x + (10 - 2x) = 0\) | Original equation |
| \(3x + (-2x + 10) = 0\) | Commutative Property of Addition |
| \((3x - 2x) + 10 = 0\) | Associative Property of Addition |
| \(x + 10 = 0\) | Simplification |
| \(x + 10 + (-10) = 0 + (-10)\) | Addition Property of Equality |
| \(x = -10\) | Simplification |

In summary:
- **Blank space 1**: Commutative Property of Addition
- **Blank space 2**: Associative Property of Addition
- **Blank space 3**: Addition Property of Equality

This dotted format will help clearly distinguish each step and its justification.