Question

simplify each expression. for exercises 1–4 and 9–12, write your answer in factored form. (examples 1–3)

1. $3(x + 4) + 5x$ 2. $-4(x + 1) + 6x$ 3. $-5(2x - 6) + 25x$
2. $2(-8x - 3) + 18x$ 5. $\frac{1}{6}x + \frac{3}{4}(\frac{1}{2}x - 4)$ 6. $\frac{2}{3}(6x - \frac{1}{6}) + 3x$
3. $\frac{5}{8}x + \frac{1}{2}(\frac{1}{4}x + 10)$ 8. $\frac{2}{5}(10x + \frac{3}{4}) - 2x$ 9. $\frac{3}{4}(24x + 28) - (4x$
4. $-\frac{1}{2}(32x - 40) + (20x - 4)$ 11. $\frac{2}{3}(9x - 15) - (-6x + 2)$ 12. $-\frac{4}{5}(30x - 40) +$

Explanation:

1. Problem 1:

Step1: Distribute the 3

$3x + 12 + 5x$

Step2: Combine like terms

$8x + 12 = 4(2x + 3)$

2. Problem 2:

Step1: Distribute the -4

$-4x - 4 + 6x$

Step2: Combine like terms

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

3. Problem 3:

Step1: Distribute the -5

$-10x + 30 + 25x$

Step2: Combine like terms

$15x + 30 = 15(x + 2)$

4. Problem 4:

Step1: Distribute the 2

$-16x - 6 + 18x$

Step2: Combine like terms

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

5. Problem 5:

Step1: Distribute the $\frac{3}{4}$

$\frac{1}{6}x + \frac{3}{8}x - 3$

Step2: Combine like terms

$\frac{4}{24}x + \frac{9}{24}x - 3 = \frac{13}{24}x - 3$

6. Problem 6:

Step1: Distribute the $\frac{2}{3}$

$4x - \frac{1}{9} + 3x$

Step2: Combine like terms

$7x - \frac{1}{9}$

7. Problem 7:

Step1: Distribute the $\frac{1}{2}$

$\frac{5}{8}x + \frac{1}{8}x + 5$

Step2: Combine like terms

$\frac{6}{8}x + 5 = \frac{3}{4}x + 5$

8. Problem 8:

Step1: Distribute the $\frac{2}{5}$

$4x + \frac{3}{10} - 2x$

Step2: Combine like terms

$2x + \frac{3}{10}$

9. Problem 9 (partial):

Step1: Distribute the $\frac{3}{4}$

$18x + 21 - 4x$

Step2: Combine like terms

$14x + 21 = 7(2x + 3)$

10. Problem 10:

Step1: Distribute the $-\frac{1}{2}$

$-16x + 20 + 20x - 4$

Step2: Combine like terms

$4x + 16 = 4(x + 4)$

11. Problem 11:

Step1: Distribute terms

$6x - 10 + 6x - 2$

Step2: Combine like terms

$12x - 12 = 12(x - 1)$

12. Problem 12 (partial):

Step1: Distribute the $-\frac{4}{5}$

$-24x + 32$

Answer:

1. $4(2x + 3)$
2. $2(x - 2)$
3. $15(x + 2)$
4. $2(x - 3)$
5. $\frac{13}{24}x - 3$
6. $7x - \frac{1}{9}$
7. $\frac{3}{4}x + 5$
8. $2x + \frac{3}{10}$
9. $7(2x + 3)$ (completed from partial expression)
10. $4(x + 4)$
11. $12(x - 1)$
12. $-24x + 32$ (completed from partial expression)