Question

1) -(x + 1) - (2x - 3) - (x + 4) 2) 4 (y - 3) - (y + 3) 3) 2 (x + 3) + 4 (x - 1) 4) 4 (x - 10) + 4x - 2 (x -1) 5) -2 (k + 1) - (1 - k)

Answer 1

1) -(x + 1) - (2x - 3) - (x + 4) = -x - 1 - 2x + 3 - x - 4 = -4x - 2

2) 4 (y - 3) - (y + 3) = 4y - 12 - y - 3 = 3y - 15

3) 2 (x + 3) + 4 (x - 1) = 2x + 6 + 4x - 4 = 6x + 2

4) 4 (x - 10) + 4x - 2 (x -1) = 4x - 40 + 4x - 2x + 2 = 6x - 38

5) -2 (k + 1) - (1 - k) = -2k - 2 - 1 + k = -k - 3

Answer 2

Let's simplify each of the expressions:

1. -(x + 1) - (2x - 3) - (x + 4)

To simplify this, distribute the negative sign in each parenthesis and combine like terms:

= -x - 1 - 2x + 3 - x - 4 = -x - 2x - x - 1 + 3 - 4 = -4x - 2

2. 4(y - 3) - (y + 3)

To simplify this, distribute the 4 in the first parenthesis and then combine like terms:

= 4y - 12 - y - 3 = 4y - y - 12 - 3 = 3y - 15

3. 2(x + 3) + 4(x - 1)

To simplify this, distribute the 2 and 4 in their respective parentheses and then combine like terms:

= 2x + 6 + 4x - 4 = 2x + 4x + 6 - 4 = 6x + 2

4. 4(x - 10) + 4x - 2(x - 1)

To simplify this, distribute the 4 and -2 in their respective parentheses and then combine like terms:

= 4x - 40 + 4x - 2x + 2 = 4x + 4x - 2x - 40 + 2 = 6x - 38

5. -2(k + 1) - (1 - k)

To simplify this, distribute the -2 and -1 in their respective parentheses and then combine like terms:

= -2k - 2 - 1 + k = -2k + k - 2 - 1 = -k - 3

So, the simplified expressions are:

1. -4x - 2
2. 3y - 15
3. 6x + 2
4. 6x - 38
5. -k - 3