Question

directions: rewrite as a sum and simplify. show all your work

1. $2(x - 2)-5$
2. $3(-2x + 1)-7$
3. $4(3x - 4)-2$
4. $2(-x + 1)-2x$
5. $3(-3x + 3)-9$
6. $5(x - 4)-3x + 1$

Explanation:

1. Problem 1: $2(x-2)-5$

Step1: Distribute the 2

$2(x-2) = 2x - 4$

Step2: Rewrite as sum, combine constants

$2x - 4 - 5 = 2x + (-4) + (-5) = 2x - 9$

2. Problem 2: $3(-2x+1)-7$

Step1: Distribute the 3

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

Step2: Rewrite as sum, combine constants

$-6x + 3 - 7 = -6x + 3 + (-7) = -6x - 4$

3. Problem 3: $4(3x-4)-2$

Step1: Distribute the 4

$4(3x-4) = 12x - 16$

Step2: Rewrite as sum, combine constants

$12x - 16 - 2 = 12x + (-16) + (-2) = 12x - 18$

4. Problem 4: $2(-x+1)-2x$

Step1: Distribute the 2

$2(-x+1) = -2x + 2$

Step2: Rewrite as sum, combine like terms

$-2x + 2 - 2x = -2x + (-2x) + 2 = -4x + 2$

5. Problem 5: $3(-3x+3)-9$

Step1: Distribute the 3

$3(-3x+3) = -9x + 9$

Step2: Rewrite as sum, combine constants

$-9x + 9 - 9 = -9x + 9 + (-9) = -9x$

6. Problem 6: $5(x-4)-3x+1$

Step1: Distribute the 5

$5(x-4) = 5x - 20$

Step2: Rewrite as sum, combine like terms

$5x - 20 - 3x + 1 = 5x + (-3x) + (-20) + 1 = 2x - 19$

Answer:

1. $2x - 9$
2. $-6x - 4$
3. $12x - 18$
4. $-4x + 2$
5. $-9x$
6. $2x - 19$