Question

heya ppl ❗️❗️❗️

⭐️_________

solve these inequtions

1) l x-1 l +3 / l x-1 l +4 ≥ 0
2) l x-3l -4 / l x-3 l +3 < 0
3) l x+3 l +x / x+2 > 1​

Answer 1

Hey mate,

1)

Since the denominator is +ve,

So just cross multiply,

So, we get,

|x-1| + 3 >= 0

|x-1| >= - 3

So we will open the mod with + ve and - ve,

x - 1 >= - 3

x >= - 2...(1)

And,

x-1 <= -3

x <= - 2...(2)

FROM (1) and (2),

x = - 2

2)

Same as above,

|x-3| - 4 < 0

We will open the mod with +ve and - ve,

x < 7...(1)

And

x > - 1...(2)

From (1) and (2),

x belongs to (-1,7)

3) For this problem let's open the mod from the first step only,

x + 3 > 2

x > - 1...(1)

And,

x + 3 < - 2

x < - 5...(2)

From (1) and (2),

x belongs to (-1,inf) U (-5,inf)

Hope this helps you out!

Answer 2

$\huge{Heya\:Riddhi\:Dii}$

answer in attachment...