^{need linear graphing step by step showig graphing as well...}

*Solving inequality is very like solving equation. The only difference: if divide or multiply both sides of inequality by negative number, we have to change sign of inequality to opposite.*

*~~~~~~~~~~**8 – x > 15*

**1.**− 8 − 8

− x

**7**

*>*÷(- 1) ÷(- 1)

**x < - 7**, or all real numbers out of interval

**(- ∞, - 7)***o———|————>*

**<====|=====**-

**10 + ∞**

*∞ - 10 - 7*Let's verify the answer:

*for x = -10,*

8 - (-10) > 15

8 + 10 > 15

18 > 15 (

*True*)

*for x = 10,*

8 - 10 > 15

- 2 > 15 (

*False*)

**6x - 13 > 11**

*2.*+ 13 + 13

6x > 24

÷ 6 ÷ 6

*, or all real numbers out of interval*

**x > 4**

*(4, + ∞)*<---------|----o

*======|=====>*− ∞ 0

*4 10 + ∞*Check the answer:

for x = 0,

6*0 - 13 > 11

- 13 > 11 (

*False*)

for x = 10,

6*10 - 13 > 11

60 - 13 > 11

47 > 11 (

*True*)

**- 9 < - 1 + 4x < 15**

*3.*+ 1 + 1 + 1

- 8 < 4x < 16

÷ 4 ÷ 4 ÷ 4

**, or all real numbers out of interval**

*- 2 < x < 4*

**(-2, 4)**<- -----|-----o

**o-----|------>**

*====|======*− ∞ − 3 − 2 0 4 6 + ∞

Check the answer:

*for x = - 3,*

- 9 < - 1 + 4*(-3) < 15

- 9 < -13 < 15 (

*False*)

( - 9 > - 13) !!!

*for x = 0,*

- 9 < - 1 + 4*0 < 15

- 9 < 3 < 15 (

*True*)

for x = 6,

- 9 < - 1 + 4*6 < 15

- 9 < 23 < 15 (

*False*)

( 23 > 15 ) !!!