Question 331404
<font face="Garamond" size="+2">I think you mean


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |5a|\ \leq\ 20]


That symbol means "less than or equal" not "lesser and equel"


Use the definition of absolute value:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ |x|\ =\ \left\{\ \ x\text{ if }x\ \geq\ 0\cr-x\text{ if }x\ <\ \,0\right]


So:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 5a\ \leq\ 20\ \ \Rightarrow\ \ a\ \leq\ 4]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -5a\ \leq\ 20\ \ \Rightarrow\ \ a\ \geq\ -4]


Which two expressions can be combined to form:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -4\ \leq\ a\ \leq\ 4]


Or specified in interval notation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \[-4,4\]]


Or specified in Set Builder notation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \{a\,|\,a\,\in\,\mathbb{R},\,-4\,\leq\,a\,\leq\, 4\}]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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