Solve absolute value inequality :

5>|4-x|

5>|4-x|

quiquenobi2v6
2021-12-17
Answered

Solve absolute value inequality :

5>|4-x|

5>|4-x|

You can still ask an expert for help

Charles Benedict

Answered 2021-12-18
Author has **32** answers

Step 1

Given

5>|4-x|

Switch sides

|4-x|<5...(1)

Apply absolute rule |u|− then -a<u<a

Step 2

from (1)

-5<4-x<5

$\Rightarrow 4-x\succ 5$

$\Rightarrow 4\succ 5+x$

$\Rightarrow 4+5>x$

$\Rightarrow x<9$

and

4-x<5

4<5+x

4-5<x

-1<x

$\Rightarrow x\succ 1$

Step 3

combine intervals

x<9 and x>-1

merge overlapping interval

-1<x<9

Interval notation : (−1,9)

Given

5>|4-x|

Switch sides

|4-x|<5...(1)

Apply absolute rule |u|− then -a<u<a

Step 2

from (1)

-5<4-x<5

and

4-x<5

4<5+x

4-5<x

-1<x

Step 3

combine intervals

x<9 and x>-1

merge overlapping interval

-1<x<9

Interval notation : (−1,9)

Gerald Lopez

Answered 2021-12-19
Author has **29** answers

Given,

5>|4-x|

On simplification, we get

5>|4-x|

$\Rightarrow |4-x|<5$

$\Rightarrow -5<4-x<5\text{}\text{}\text{}[\therefore \left|x\right|a\Rightarrow -axa]$

$\Rightarrow -5-4<4-x-4<5-4$ [Subtracting 4]

$\Rightarrow -9<-x<1$

$\Rightarrow \frac{-9}{-1}>\frac{-x}{-1}>\frac{1}{-1}$ [Dividing -1. When divided by a negative number, the sign will get reversed.]

$\Rightarrow 9>x\succ 1$

$\Rightarrow -1<x<9$

$\Rightarrow x\in (-1,9)$

5>|4-x|

On simplification, we get

5>|4-x|

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