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If ||x+3| - 12| < 13, what is the range of x? Options

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by deloitte247 » Sat Aug 17, 2019 8:50 am
If || x + 3 | - 12 | < 13 what is the range of x ?
Let | x + 3 | = y
| y - 12 | < 13
Range of x for which | y - 12 | < 13 is -13 < y - 12 < 13
-13 + 12 < y - 12 + 12 < 13 + 12
-1 < y < 25 where y = | x + 3 |
-1 < | x + 3 | < 25 even if x = 0, the value of x + 3 will always be greater than zero
$$Therefore,\ 0\le\left|x+3\right|<25$$
Then the range of x will be ; -25 < x + 3 < 25
-25 - 3 < x + 3 - 3 < 25 - 3
-28 < x < 22
Hence, range of x = ( -28, 22 )
Answer = option C
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by swerve » Sat Aug 17, 2019 2:41 pm
\(|x+3|\) will always be positive. Therefore \(|x+3|<25\) in order for \(||x+3|- 12|< 13\) to be true!

\(|x+3|<25 \Rightarrow -28 < x < 22\)

Therefore, __C__
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