Drag justifications into the table to explain each step in solving the equation 5 left-parenthesis 2 x plus 1 right-parenthesis equals 2 left-parenthesis 4 x minus 7 right-parenthesis plus 3.

Question

Response area with 5 blank spaces
Step Justifications
5 left-parenthesis 2 x plus 1 right-parenthesis equals 2 left-parenthesis 4 x minus 7 right-parenthesis plus 3 given
10 x plus 5 equals 8 x minus 14 plus 3
Blank space 1 empty

10 x plus 5 equals 8 x minus 11
Blank space 2 empty

2 x plus 5 equals negative 11
Blank space 3 empty

2 x equals negative 16
Blank space 4 empty

x equals negative 8
Blank space 5 empty




Answer options with 7 options.

Answer 1

Here are the justifications for each step in solving the equation:

| Step | Justifications | |--------------------------------------------------------|------------------------------------------------| | 5(2x + 1) = 2(4x - 7) + 3 | given | | 10x + 5 = 8x - 14 + 3 | Distributive property (5 * (2x + 1) and 2 * (4x - 7)) | | 10x + 5 = 8x - 11 | Combine like terms (-14 + 3 = -11) | | 2x + 5 = -11 | Subtract 8x from both sides (10x - 8x = 2x) | | 2x = -16 | Subtract 5 from both sides (5 - 5 = 0) | | x = -8 | Divide both sides by 2 |

Drag justifications into the table:

1. Blank space 1: Distributive property (5 * (2x + 1) and 2 * (4x - 7))
2. Blank space 2: Combine like terms (-14 + 3 = -11)
3. Blank space 3: Subtract 8x from both sides (10x - 8x = 2x)
4. Blank space 4: Subtract 5 from both sides (5 - 5 = 0)
5. Blank space 5: Divide both sides by 2

This completes the justification for each of the steps in solving the equation.