I need some help with algebra 2 :s?

Question

heres some questions that i dont know how to solve. im pretty sure they all have the same principle but ya...... if you could plz explain how you find the answer

1.

| y + 5 | < 2

--|--|--|--|--|--|---|---|---|--

-8-7-6-5-4-3 -2 -1 0

2.

| 2z - 2 < 3 <------( the "<" is underlined)

--|--|--|--|--|--|--|--|--|--

3

| x | > x - 1

--|--|--|--|--|--|--|--|--|--|--

4.

| 3n - 2 | - 2 < 1

--|--|--|--|--|--|--|--|--|--|--

thank you .

Answer 1

I guess number 1) and 2)  (number 2 you missed the | sigen after 2) are the same, I would do # 1)

1)   |y + 5| &lt; 2  (this means in between -2 and 2), therefore

the given inequality can be written as:

-2 &lt; y + 5 &lt; 2

- 2 - 5 &lt; y &lt; 2 - 5   (subtract 5 for 3 parts)

- 7 &lt; y &lt; - 3 is the answer

that means y is in between -7 and -3

--|--|==|==|==|==|---|---|---|-- y

-8-7 -6  -5  -4 -3   -2  -1  0

3)  | x | &gt; x - 1

the given inequality can be written as 2 inequalities combine:

(1) x &gt; x - 1 or (2) -x &gt; x - 1

From (1) we have:

x &gt; x - 1

0x &gt; 1     cannot find any x satisfy with this inequality

therefore no solution

From (2) -x &gt; x - 1

0 &gt; 2x - 1  (+x both sides)

1 &gt; 2x        (+1 both sides)

1/2 &gt; x or x &lt; 1/2  is solution.

==|==|==|==|==|=.-|--|--

___________-1/2 0  1

4) this inquality will be as same as #1 and #2, since

| 3n - 2 | - 2 &lt; 1

  | 3n - 2 | - 2 + 2 &lt; 1 + 2

  |3n - 2| &lt; 3 or

- 3 &lt; 3n - 2 &lt; 3     (is in between), or

-3 + 2 &lt; 3n -2 +2 &lt; 3 + 2

  - 1     &lt;  3n  &lt; 5, or

-1/3  &lt; n &lt; 5/3   (divide all by 3)

is the answer.