Question

Step 1Solve absolute value inequality.-4 abs(1 - x)< -16

Matrices
ANSWERED
asked 2021-01-27

Step 1
Solve absolute value inequality.
\(\displaystyle-{4}{\left|{{1}-{x}}\right|}{<}-{16}\)

Answers (1)

2021-01-28

Step 1
Solve absolute value inequality.
\(\displaystyle-{4}{\left|{{1}-{x}}\right|}{<}-{16}\)
Step 2
We have, \(\displaystyle-{4}{\left|{{1}-{x}}\right|}{<}-{16}\)
\(\displaystyle\Rightarrow-{4}{\left|{{1}-{x}}\right|}{<}-{16}\)
\(\displaystyle\Rightarrow-{4}{\left({\left|{-{x}+{1}}\right|}\right)}{<}-{16}\)
Dividing both sides by -4 ,we get
\(\displaystyle\Rightarrow\frac{{-{4}{\left({\left|{-{x}+{1}}\right|}\right)}}}{{-{4}}}{<}\frac{{-{16}}}{{-{4}}}\)
\(\displaystyle\Rightarrow{\left|{-{x}+{1}}\right|}{>}{4}\)
Now,solving for absolute value.
We know either, -x+1>4 or -x+1<-4
Possibility(1)
-x+1>4
\(\displaystyle\Rightarrow-{x}+{1}-{1}{>}{4}-{1}\)
\(\displaystyle\Rightarrow-{x}{>}{3}\)
Divide both sides by -1,we get
\(\displaystyle\Rightarrow\frac{{-{x}}}{{-{1}}}{>}\frac{{3}}{{-{1}}}\)
\(\displaystyle\Rightarrow{x}{<}-{3}\)
Possibility(2)
-x+1<-4
Subtract 1 from both sides,we get
\(\displaystyle\Rightarrow\frac{{-{x}}}{{-{1}}}{<}\frac{{-{5}}}{{-{1}}}\)
\(\displaystyle\Rightarrow{x}{>}{5}\)
Hence, x<-3 or x>5

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