lх+5l + lx+8l=13lxl-lx-2l=2. Created by lina5711. algebra-ru

lх+5l + lx+8l=13lxl-lx-2l=2...

lina5711 @lina5711

August 2022 1 6 Report

lх+5l + lx+8l=13

lxl-lx-2l=2

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NNNLLL54

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$1)\; \; |x+5|+|x+8|=13\\\\x+5=0\; \; ,\; \; x=-5\\\\x+8=0\; \; ,\; \; x=-8\\\\------(-8)-----(-5)------\\\\a)\; \; x\leq -8:\; |x+5|=-x-5\; ,\; |x+8|=-x-8\\\\-x-5-x-8=13\; ,\; \; -2x=26\; ,\; \; \underline {x=-13}\in (-\infty ,-8\, ]\\\\b)\; \; -8-5\; :\; \; |x+5|=x+5\; ,\; |x+8|=x+8\; ,\\\\x+5+x+8=13\; ,\; \; 2x=0\; ,\; \underline {x=0}\in (-5,+\infty )\\\\Otvet:\; \; x_1=-13\; ,\; x_2=0\; .$

$2)\; \; |x|-|x-2|=2\\\\x=0\; \; ,\\\\x-2=0\; \; ,\; \; x=2\\\\------(0)-----(2)------\\\\a)\; \; x\leq 0\; :\; |x|=-x\; ,\; |x-2|=-x+2\\\\-x-(-x+2)=2\; ,\; \; -2=2\; neverno\; ,\; \; x\in \varnothing \\\\b)\; \; 02\; :\; \; |x|=x\; ,\; |x-2|=x-2\; ,\\\\x-(x-2)=2\; ,\; \; 2=2\; ,\; verno\; \; ,\underline {x\in (2,+\infty )}\\\\Otvet:\; \; x\in [\, 2,+\infty )\; .$

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