Question

$\left|3+2x\right|\le \:7$

solve it

Answer 1

$\left|3+2x\right|\le \:7\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-5\le \:x\le \:2\:\\ \:\mathrm{Interval\:Notation:}&\:\left[-5,\:2\right]\end{bmatrix}$

$\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:\le \:a,\:a\:>\:0\:\mathrm{then}\:-a\:\le \:u\:\le \:a$

$-7\le \:3+2x\le \:7$

$3+2x\ge \:-7\quad \mathrm{and}\quad \:3+2x\le \:7$

$3+2x\ge \:-7\quad :\quad x\ge \:-5$

$3+2x\le \:7\quad :\quad x\le \:2$

$\mathrm{Combine\:the\:intervals}$

$x\ge \:-5\quad \mathrm{and}\quad \:x\le \:2$

$\mathrm{Merge\:Overlapping\:Intervals}$

$-5\le \:x\le \:2$

Answer 2

Answer:

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