Question 637426
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0\ <\ 4\ +\ 2x\ <\ 22]


for "and" compound inequalties, do it just like a regular single variable equation, except whatever you do to one part, you have to do to all three parts.  Add -4 to all three parts:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -4\ <\ 2x\ <\ 18]


Multiply all three parts by *[tex \LARGE \frac{1}{2}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -2\ <\ x\ <\ 9]


for "or" compound inequalties, solve each part separately:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3x\ +\ 6\ <\ -3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 3x\ <\ -9]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ <\ -3]


Then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 5\ -\ x\ <\ 1]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -x\ <\ -4]


Multiply by -1.  Since the multiplier is < 0, reverse the sense of the inequality:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ >\ 4]


Then state both parts with the "or"


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\ < -3\ \ ] or *[tex \LARGE x\ >\ 4]


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