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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
Question
Solve the following for $x$, where $|x|$ is modulus function, $[x]$ is the greatest integer function, $\{x\}$ is a fractional part function.

$|x+4| \geq 5$

✓

Answer

$|x+4| \geq 5$
The solution of $|x| \geq a$ is $x \leq-a$ or $x \geq a$
$\therefore|x+4| \geq 5$ gives
$\therefore \mathrm{x}+4 \leq-5$ or $\mathrm{x}+4 \geq 5$
$\therefore \mathrm{x} \leq-5-4$ or $\mathrm{x} \geq 5-4$
$\therefore \mathrm{x} \leq-9$ or $\mathrm{x} \geq 1$
$\therefore$ The solution set $=(-\infty,-9] \cup[1, \infty)$

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