Select all the expressions that are equivalent to 10w - 8 + 6 - 4w.

2(3w - 1)
(6w + 3) + (2w - 7)
6w - 2
(11w - 1) - (5w + 3)
3w + 7 + 3w - 9
14w + 14
2(5w + 7)

10w - 8 + 6 - 4w = 6 w - 2

2 ( 3 w - 1 ) = 2 ∙ 3 w + 2 ∙ ( - 1 ) = 6 w - 2

Correct

( 6 w + 3 ) + ( 2 w - 7 ) =

6 w + 3 + 2 w - 7 = 8 w - 4

Incorrect

6w - 2 = 6w - 2

Correct

( 11 w - 1 ) - ( 5 w + 3 ) =

11 w - 1 - 5 w + 3 = 6 w + 2

Incorrect

3 w + 7 + 3 w - 9 = 6 w - 2

Correct

14w + 14 ≠ 6 w - 2

Incorrect

2 ( 5 w + 7 ) = 2 ∙ 5 w + 2 ∙ 7 = 10 w + 14

Incorrect

All the expressions that are equivalent to 10w - 8 + 6 - 4w:

2 ( 3 w - 1 ) , 6w - 2 , 3 w + 7 + 3 w - 9

To determine which expressions are equivalent to 10w - 8 + 6 - 4w, we can simplify each expression and see if they result in the same expression.

Expression 1: 2(3w - 1)
In this expression, we distribute the 2 to both terms inside the parentheses:
2(3w) - 2(1) = 6w - 2
This expression is not equivalent to 10w - 8 + 6 - 4w.

Expression 2: (6w + 3) + (2w - 7)
In this expression, we use the distributive property to simplify:
6w + 3 + 2w - 7 = 8w - 4
This expression is not equivalent to 10w - 8 + 6 - 4w.

Expression 3: 6w - 2
This expression is already simplified and matches 10w - 8 + 6 - 4w.
Therefore, this expression is equivalent to 10w - 8 + 6 - 4w.

Expression 4: (11w - 1) - (5w + 3)
In this expression, we use the distributive property to simplify:
11w - 1 - 5w - 3 = 6w - 4
This expression is not equivalent to 10w - 8 + 6 - 4w.

Expression 5: 3w + 7 + 3w - 9
In this expression, we combine like terms:
3w + 3w + 7 - 9 = 6w - 2
This expression is not equivalent to 10w - 8 + 6 - 4w.

Expression 6: 14w + 14
This expression is not simplified and does not match 10w - 8 + 6 - 4w.
Therefore, this expression is not equivalent to 10w - 8 + 6 - 4w.

Expression 7: 2(5w + 7)
In this expression, we distribute the 2 to both terms inside the parentheses:
2(5w) + 2(7) = 10w + 14
This expression is not equivalent to 10w - 8 + 6 - 4w.

The expressions equivalent to 10w - 8 + 6 - 4w are:
- 6w - 2 (Expression 3).

To determine which expressions are equivalent to 10w - 8 + 6 - 4w, we need to simplify each expression and check if it is equal to 10w - 8 + 6 - 4w.

Let's simplify each expression one by one:

1. 2(3w - 1):
Distribute the 2 into the parentheses: 2 * 3w - 2 * 1 = 6w - 2
This expression is not equivalent to 10w - 8 + 6 - 4w.

2. (6w + 3) + (2w - 7):
Combine like terms within each parentheses: 6w + 3 + 2w - 7
Combine like terms: (6w + 2w) + (3 - 7) = 8w - 4
This expression is not equivalent to 10w - 8 + 6 - 4w.

3. 6w - 2:
This expression is not equal to 10w - 8 + 6 - 4w.

4. (11w - 1) - (5w + 3):
Apply the distributive property by multiplying -1 to each term inside the second parentheses: 11w - 1 - 5w - 3
Combine like terms: (11w - 5w) + (-1 - 3) = 6w - 4
This expression is not equivalent to 10w - 8 + 6 - 4w.

5. 3w + 7 + 3w - 9:
Combine like terms: 3w + 3w + 7 - 9 = 6w - 2
This expression is equivalent to 10w - 8 + 6 - 4w.

6. 14w + 14:
This expression is not equal to 10w - 8 + 6 - 4w.

7. 2(5w + 7):
Distribute the 2 into the parentheses: 2 * 5w + 2 * 7 = 10w + 14
This expression is not equivalent to 10w - 8 + 6 - 4w.

Therefore, the expression 3w + 7 + 3w - 9 is equivalent to 10w - 8 + 6 - 4w.