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if-K-x-R-2x-1-2x-1-0-and-J-x-R-x-2x-1-1-find-J-K-




Question Number 74455 by Mr. K last updated on 24/Nov/19
if K=(x∈R 2x−1+∣2x−1∣=0 )and  J=(x∈R −x(2x+1)≤−1) find J−K.
$${if}\:{K}=\left({x}\in\mathbb{R}\:\mathrm{2}{x}−\mathrm{1}+\mid\mathrm{2}{x}−\mathrm{1}\mid=\mathrm{0}\:\right){and} \\ $$$${J}=\left({x}\in\mathbb{R}\:−{x}\left(\mathrm{2}{x}+\mathrm{1}\right)\leqslant−\mathrm{1}\right)\:{find}\:{J}−{K}. \\ $$
Answered by MJS last updated on 24/Nov/19
K={x∈R∣x≤(1/2)}  J={x∈R∣x≤−1∨x≥(1/2)}  J−K={x∈R∣x∈J∧x∉K}={x∈R∣x>(1/2)}
$${K}=\left\{{x}\in\mathbb{R}\mid{x}\leqslant\frac{\mathrm{1}}{\mathrm{2}}\right\} \\ $$$${J}=\left\{{x}\in\mathbb{R}\mid{x}\leqslant−\mathrm{1}\vee{x}\geqslant\frac{\mathrm{1}}{\mathrm{2}}\right\} \\ $$$${J}−{K}=\left\{{x}\in\mathbb{R}\mid{x}\in{J}\wedge{x}\notin{K}\right\}=\left\{{x}\in\mathbb{R}\mid{x}>\frac{\mathrm{1}}{\mathrm{2}}\right\} \\ $$

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