Question

please help me this question​

Answer 1

Answer:

x is greater than 3 or less than -5

Step-by-step explanation:

Case 1

x + 1 greater than 4

x greater than 4-1

x greater than 3

Case 2

-(x + 1) greater than 4

x + 1 less than -4

x less than -5

Therefore

x is greater than 3 or less than -5

Answer 2

Solution:

Given Inequality:

$\rm \longrightarrow |x + 1| > 4, x \in R$

There can be two possible cases:

$\rm 1. \: x + 1 > 4, x +1> 0$

$\rm 2. - ( x + 1 )> 4, x +1< 0$

Solving (1):

$\rm \longrightarrow x + 1 > 4$

$\rm \longrightarrow x + 1 - 1 >4 - 1$

$\rm \longrightarrow x >3$

$\rm \longrightarrow x \in (3, \infty]$

Solving (2):

$\rm \longrightarrow - ( x + 1 )>4$

$\rm \longrightarrow ( x + 1 ) < - 4$

$\rm \longrightarrow x + 1 - 1 < - 4 - 1$

$\rm \longrightarrow x < -5$

$\rm \longrightarrow x \in [ - \infty, - 5)$

Combining both, we get:

$\rm \longrightarrow x \in [ - \infty, - 5) \cup (3, \infty]$

★ Which is our required answer.

Answer:

$\rm \hookrightarrow x \in [ - \infty, - 5) \cup (3, \infty]$

Note:

Absolute value is defined as:

$\rm\longrightarrow |x| = \begin{cases}\rm x\: if\: x > 0\\ \rm -x\: if\: x < 0\end{cases}$