Solve absolute value inequality. −4|1−x|&lt;−16

Question

Solve absolute value inequality. −4|1−x|&amp;lt;−16

yunitsiL · Accepted Answer

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

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Solve absolute value inequality.-4|1-x|<-16

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