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

Question

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.