![\"\"](\"https:\/\/dpanagiotis.sites.sch.gr\/wp-content\/uploads\/2019\/06\/absolute-value-of-a-300x177.png\")
![\"|a|=a\"](\"https:\/\/dpanagiotis.sites.sch.gr\/wp-content\/ql-cache\/quicklatex.com-f062ab438cfb057310ce8a7116898266_l3.png\" "\\"Rendered")
\u03b1\u03bd a>0![\"|a|=0\"](\"https:\/\/dpanagiotis.sites.sch.gr\/wp-content\/ql-cache\/quicklatex.com-d3147d494f7f8c513bb41bcb5663829a_l3.png\" "\\"Rendered")
\u03b1\u03bd a=0![\"|a|=-a\"](\"https:\/\/dpanagiotis.sites.sch.gr\/wp-content\/ql-cache\/quicklatex.com-980af754df4b5628d30e10cbd82c3941_l3.png\" "\\"Rendered")
\u03b1\u03bd a<0<\/p>\n\u03a3\u03c4\u03bf \u03ac\u03c1\u03b8\u03c1\u03bf \u03b1\u03c5\u03c4\u03cc \u03b8\u03b1 \u03b4\u03bf\u03cd\u03bc\u03b5 \u03bc\u03b5 \u03c4\u03b7 \u03b2\u03bf\u03ae\u03b8\u03b5\u03b9\u03b1 \u03bc\u03b9\u03b1\u03c2 \u03ac\u03c3\u03ba\u03b7\u03c3\u03b7\u03c2 \u03c4\u03b9 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03ba\u03ac\u03bd\u03bf\u03c5\u03bc\u03b5 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b1\u03c0\u03b1\u03bb\u03bb\u03b1\u03b3\u03bf\u03cd\u03bc\u03b5 \u03b1\u03c0\u03cc \u03c4\u03b9\u03c2 \u03b1\u03c0\u03cc\u03bb\u03c5\u03c4\u03b5\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03cc\u03c4\u03b1\u03bd \u03b1\u03c5\u03c4\u03cc \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c0\u03b1\u03c1\u03b1\u03af\u03c4\u03b7\u03c4\u03bf.<\/p>\n
\u039a\u03b1\u03c4\u0384\u03b1\u03c1\u03c7\u03ac\u03c2 \u03b1\u03c2 \u03b8\u03c5\u03bc\u03b7\u03b8\u03bf\u03cd\u03bc\u03b5 \u03c0\u03c9\u03c2 \u03bf\u03c1\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b7 \u03b1\u03c0\u03cc\u03bb\u03c5\u03c4\u03b7 \u03c4\u03b9\u03bc\u03ae \u03b5\u03bd\u03cc\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03bf\u03cd: \u03b1\u03bd a>0 \u03b1\u03bd a=0 \u03b1\u03bd a<0<\/p>\n
\u0392\u03bb\u03ad\u03c0\u03bf\u03c5\u03bc\u03b5 \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd \u03cc\u03c4\u03b9 \u03b3\u03b9\u03b1 \u03bd\u03b1 \u03b1\u03c0\u03b1\u03bb\u03bb\u03b1\u03b3\u03bf\u03cd\u03bc\u03b5 \u03b1\u03c0\u03cc \u03c4\u03b1 \u03b1\u03c0\u03cc\u03bb\u03c5\u03c4\u03b1 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03b1\u03bd \u03c4\u03bf \u03c0\u03b5\u03c1\u03b9\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03bf \u03c4\u03b7\u03c2 \u03b1\u03c0\u03cc\u03bb\u03c5\u03c4\u03b7\u03c2 \u03c4\u03b9\u03bc\u03ae\u03c2 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b8\u03b5\u03c4\u03b9\u03ba\u03cc, \u03bc\u03b7\u03b4\u03ad\u03bd \u03ae \u03b1\u03c1\u03bd\u03b7\u03c4\u03b9\u03ba\u03cc \u03b3\u03b9\u03b1\u03c4\u03af \u03c3\u03b5 \u03ba\u03ac\u03b8\u03b5 \u03c0\u03b5\u03c1\u03af\u03c0\u03c4\u03c9\u03c3\u03b7 \u03b5\u03bd\u03b5\u03c1\u03b3\u03bf\u03cd\u03bc\u03b5 \u03b4\u03b9\u03b1\u03c6\u03bf\u03c1\u03b5\u03c4\u03b9\u03ba\u03ac.<\/p>\n
\u0393\u03b9\u03b1 \u03c0\u03b1\u03c1\u03ac\u03b4\u03b5\u03b9\u03b3\u03bc\u03b1, \u03b1\u03bd x<3 \u03c4\u03cc\u03c4\u03b5 ![\"|x-3|=-(x-3)=3-x\"](\"https:\/\/dpanagiotis.sites.sch.gr\/wp-content\/ql-cache\/quicklatex.com-e20325e311c68a34da72ffa30eb0b882_l3.png\" "\\"Rendered")
\u03ba\u03b9 \u03b1\u03c5\u03c4\u03cc \u03b3\u03b9\u03b1\u03c4\u03af; \u03b3\u03b9\u03b1\u03c4\u03af \u03bc\u03b1\u03c2 \u03ad\u03c7\u03bf\u03c5\u03bd \u03b4\u03ce\u03c3\u03b5\u03b9 \u03cc\u03c4\u03b9 x<3 \u03ac\u03c1\u03b1 \u03b8\u03b1 \u03b5\u03af\u03bd\u03b1\u03b9 x-3<3-3 ![\"\Leftrightarrow\"](\"https:\/\/dpanagiotis.sites.sch.gr\/wp-content\/ql-cache\/quicklatex.com-ce8804ee38acb4fd2b01b1518fdd4a62_l3.png\" "\\"Rendered")
x-3<0\u00a0 (\u03b1\u03c6\u03b1\u03b9\u03c1\u03ad\u03c3\u03b1\u03bc\u03b5 \u03ba\u03b9 \u03b1\u03c0\u03cc \u03c4\u03b1 \u03b4\u03c5\u03bf \u03bc\u03ad\u03bb\u03b7 \u03c4\u03bf 3 \u03ce\u03c3\u03c4\u03b5 \u03bd\u03b1 \u03b4\u03b7\u03bc\u03b9\u03bf\u03c5\u03c1\u03b3\u03ae\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c3\u03c4\u03b7 \u03b4\u03bf\u03b8\u03b5\u03af\u03c3\u03b1 \u03b1\u03bd\u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c4\u03bf \u03c0\u03b5\u03c1\u03b9\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03bf \u03c4\u03bf\u03c5 \u03b1\u03c0\u03bf\u03bb\u03cd\u03c4\u03bf\u03c5).<\/p>\n
\u0393\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03bf\u03cd\u03bc\u03b5 \u03c4\u03ce\u03c1\u03b1 \u03bc\u03b9\u03b1 \u03ac\u03c3\u03ba\u03b7\u03c3\u03b7 \u03c0\u03ac\u03bd\u03c9 \u03c3\u03c4\u03bf \u03c3\u03c5\u03b3\u03ba\u03b5\u03ba\u03c1\u03b9\u03bc\u03ad\u03bd\u03bf \u03b8\u03ad\u03bc\u03b1.<\/p>\n
\u0386\u03c3\u03ba\u03b7\u03c3\u03b7:<\/p>\n
\u0391\u03bd -3<x<1 \u03bd\u03b1 \u03b1\u03c0\u03bb\u03bf\u03c0\u03bf\u03b9\u03ae\u03c3\u03b5\u03c4\u03b5 \u03c4\u03b7\u03bd \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 A=2|x-1|+|x+3|-3|x+4| \u03ba\u03b1\u03b9 \u03c3\u03c4\u03b7 \u03c3\u03c5\u03bd\u03ad\u03c7\u03b5\u03b9\u03b1 \u03bd\u03b1 \u03bb\u03cd\u03c3\u03b5\u03c4\u03b5 \u03c4\u03b7\u03bd \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 ![\"A+1=x^2-9x\"](\"https:\/\/dpanagiotis.sites.sch.gr\/wp-content\/ql-cache\/quicklatex.com-608d09c7de98139f4467857b6e528df5_l3.png\" "\\"Rendered")
.<\/p>\n
\u039b\u03cd\u03c3\u03b7:<\/p>\n
\u0393\u03b9\u03b1 \u03bd\u03b1 \u03b1\u03c0\u03bb\u03bf\u03c0\u03bf\u03b9\u03b7\u03b8\u03b5\u03af \u03b7 \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u0391 \u03b8\u03b1 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03c6\u03cd\u03b3\u03bf\u03c5\u03bd \u03bf\u03b9 \u03b1\u03c0\u03cc\u03bb\u03c5\u03c4\u03b5\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03ba\u03b1\u03b9 \u03bc\u03b5\u03c4\u03ac \u03bd\u03b1 \u03c3\u03c5\u03bc\u03bc\u03b1\u03b6\u03b5\u03c5\u03c4\u03b5\u03af \u03bb\u03b9\u03b3\u03ac\u03ba\u03b9. \u0393\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03b9\u03ce\u03be\u03c9 \u03c4\u03b1 \u03b1\u03c0\u03cc\u03bb\u03c5\u03c4\u03b1 \u03cc\u03bc\u03c9\u03c2 \u03b8\u03b1 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03be\u03ad\u03c1\u03c9 \u03c4\u03bf \u03c0\u03b5\u03c1\u03b9\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03bf \u03ba\u03ac\u03b8\u03b5 \u03b1\u03c0\u03bf\u03bb\u03cd\u03c4\u03bf\u03c5 \u03c4\u03b9 \u03c0\u03c1\u03cc\u03c3\u03b7\u03bc\u03bf \u03ad\u03c7\u03b5\u03b9 \u03ba\u03b9 \u03b1\u03c5\u03c4\u03cc \u03b8\u03b1 \u03c4\u03bf \u03b2\u03c1\u03c9 \u03b4\u03bf\u03c5\u03bb\u03b5\u03cd\u03bf\u03bd\u03c4\u03b1\u03c2 \u03ba\u03b1\u03c4\u03ac\u03bb\u03bb\u03b7\u03bb\u03b1 \u03c4\u03b7\u03bd \u03b1\u03bd\u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1 \u03c0\u03bf\u03c5 \u03bc\u03bf\u03c5 \u03ad\u03c7\u03bf\u03c5\u03bd \u03b4\u03ce\u03c3\u03b5\u03b9.<\/p>\n
\u03b1\u03c6\u03bf\u03cd \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 -3<x<1<\/strong> \u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03c9 \u03cc\u03c4\u03b9 -3<\u03c7<1<\/strong> \u03c0\u03c1\u03bf\u03c6\u03b1\u03bd\u03ce\u03c2 \u03b1\u03c6\u03bf\u03cd \u03c4\u03bf x+3 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b8\u03b5\u03c4\u03b9\u03ba\u03cc \u03c4\u03bf \u03af\u03b4\u03b9\u03bf \u03b8\u03b1 \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9 \u03ba\u03b1\u03b9 \u03b3\u03b9\u03b1 \u03c4\u03bf x+4 \u03c0\u03bf\u03c5 \u03b5\u03af\u03bd\u03b1\u03b9 \u03ba\u03b1\u03c4\u03ac \u03bc\u03b9\u03b1 \u03bc\u03bf\u03bd\u03ac\u03b4\u03b1 \u03bc\u03b5\u03b3\u03b1\u03bb\u03cd\u03c4\u03b5\u03c1\u03bf \u03b1\u03bb\u03bb\u03ac \u03b1\u03c2 \u03c4\u03bf \u03b4\u03bf\u03c5\u03bb\u03ad\u03c8\u03bf\u03c5\u03bc\u03b5 \u03ba\u03b9 \u03b1\u03c5\u03c4\u03cc \u03bc\u03b5 \u03c4\u03bf\u03bd \u03af\u03b4\u03b9\u03bf \u03c4\u03c1\u03cc\u03c0\u03bf. \u0395\u03af\u03bc\u03b1\u03c3\u03c4\u03b5 \u03c4\u03ce\u03c1\u03b1 \u03ad\u03c4\u03bf\u03b9\u03bc\u03bf\u03b9 \u03bd\u03b1 \u03b4\u03bf\u03cd\u03bc\u03b5 \u03c0\u03c9\u03c2 \u03b8\u03b1 \u03b3\u03af\u03bd\u03b5\u03b9 \u03b7 \u03c0\u03b1\u03c1\u03ac\u03c3\u03c4\u03b1\u03c3\u03b7 \u0391 \u03b1\u03c6\u03bf\u03cd \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bc\u03b5 \u03bd\u03b1 \u03b1\u03bd\u03c4\u03b9\u03ba\u03b1\u03c4\u03b1\u03c3\u03c4\u03ae\u03c3\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b9\u03c2 \u03b1\u03c0\u03cc\u03bb\u03c5\u03c4\u03b5\u03c2 \u03c4\u03b9\u03bc\u03ad\u03c2 \u03bc\u03b5 \u03b1\u03c5\u03c4\u03ac \u03c0\u03bf\u03c5 \u03b2\u03c1\u03ae\u03ba\u03b1\u03bc\u03b5 \u03c0\u03b1\u03c1\u03b1\u03c0\u03ac\u03bd\u03c9. \u0393\u03b9\u03b1 \u03bd\u03b1 \u03b4\u03bf\u03cd\u03bc\u03b5 \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd \u03c4\u03b9 \u03b8\u03b1 \u03c0\u03c1\u03bf\u03ba\u03cd\u03c8\u03b5\u03b9,<\/p>\n A=2|x-1|+|x+3|-3|x+4|<\/p>\n A=2(1-x)+(x+3)-3(x+4)<\/p>\n A=2-2x+x+3-3x-12<\/p>\n A=-4x-7.<\/p>\n \u038c\u03c3\u03bf\u03bd \u03b1\u03c6\u03bf\u03c1\u03ac \u03c4\u03ce\u03c1\u03b1 \u03c3\u03c4\u03bf \u03ac\u03bb\u03bb\u03bf \u03b5\u03c1\u03ce\u03c4\u03b7\u03bc\u03b1 \u03b1\u03c6\u03bf\u03cd \u03b3\u03bd\u03c9\u03c1\u03af\u03b6\u03bf\u03c5\u03bc\u03b5 \u03c4\u03bf \u0391 \u03cc\u03c4\u03b9 \u03b5\u03af\u03bd\u03b1\u03b9 \u03c4\u03bf -4x-7, \u03c4\u03bf \u03b1\u03bd\u03c4\u03b9\u03ba\u03b1\u03b8\u03b9\u03c3\u03c4\u03bf\u03cd\u03bc\u03b5 \u03ba\u03b1\u03b9 \u03bb\u03cd\u03bd\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b7\u03bd \u03b5\u03be\u03af\u03c3\u03c9\u03c3\u03b7 \u03c0\u03bf\u03c5 \u03c0\u03c1\u03bf\u03ba\u03cd\u03c0\u03c4\u03b5\u03b9. -3-1<x-1<\/span><1-1<\/strong> -4<x-1<0
<\/strong>(\u03b1\u03c6\u03b1\u03b9\u03c1\u03ad\u03c3\u03b1\u03bc\u03b5 \u03ba\u03b9 \u03b1\u03c0\u03cc \u03c4\u03b1 \u03c4\u03c1\u03af\u03b1 \u03bc\u03ad\u03bb\u03b7 \u03c4\u03b7\u03c2 \u03b1\u03bd\u03b9\u03c3\u03cc\u03c4\u03b7\u03c4\u03b1\u03c2 \u03c4\u03bf 1, \u03ce\u03c3\u03c4\u03b5 \u03bd\u03b1 \u03b4\u03b7\u03bc\u03b9\u03bf\u03c5\u03c1\u03b3\u03b7\u03b8\u03b5\u03af \u03c3\u03b5 \u03b1\u03c5\u03c4\u03ae\u03bd \u03c4\u03bf \u03c0\u03b5\u03c1\u03b9\u03b5\u03c7\u03cc\u03bc\u03b5\u03bd\u03bf \u03c4\u03bf\u03c5 \u03b1\u03c0\u03bf\u03bb\u03cd\u03c4\u03bf\u03c5 \u03c0\u03bf\u03c5 \u03bc\u03b1\u03c2 \u03b5\u03bd\u03b4\u03b9\u03b1\u03c6\u03ad\u03c1\u03b5\u03b9 \u03c4\u03bf x-1 \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae).
\u0395\u03af\u03b4\u03b1\u03bc\u03b5 \u03bb\u03bf\u03b9\u03c0\u03cc\u03bd \u03cc\u03c4\u03b9 \u03c4\u03bf x-1 \u03b5\u03af\u03bd\u03b1\u03b9 \u03b1\u03c1\u03bd\u03b7\u03c4\u03b9\u03ba\u03cc \u03ba\u03b9 \u03ad\u03c4\u03c3\u03b9 \u03c3\u03cd\u03bc\u03c6\u03c9\u03bd\u03b1 \u03bc\u03b5 \u03c4\u03bf\u03bd \u03bf\u03c1\u03b9\u03c3\u03bc\u03cc \u03c4\u03b7\u03c2 \u03b1\u03c0\u03cc\u03bb\u03c5\u03c4\u03b7\u03c2 \u03c4\u03b9\u03bc\u03ae\u03c2 \u03be\u03ad\u03c1\u03c9 \u03cc\u03c4\u03b9: |x-1|=-(x-1)=(1-x).<\/p>\n<\/li>\n\u0393\u03b9\u03b1 \u03c4\u03bf |x+3|<\/span>,<\/h4>\n
-3+3<x+3<\/span><1+3<\/strong> 0<x+3<4<\/strong>
\u03b4\u03b7\u03bb\u03b1\u03b4\u03ae x+3 \u03b8\u03b5\u03c4\u03b9\u03ba\u03cc \u03ba\u03b9 \u03ad\u03c4\u03c3\u03b9 |x+3|=(x+3).<\/p>\n<\/li>\n\u0393\u03b9\u03b1 \u03c4\u03bf |x+4|<\/span>,<\/h4>\n
-3<x<1<\/strong>-3+4<x+4<\/span><1+4<\/strong>1<x+4<5<\/strong>
\u03ba\u03b9 \u03b5\u03c0\u03bf\u03bc\u03ad\u03bd\u03c9\u03c2 |x+4|=(x+4).<\/p>\n<\/li>\n<\/ul>\n
\u0394\u03b7\u03bb\u03b1\u03b4\u03ae,<\/p>\n
![\"\[A+1=x^2-9x\Leftrightarrow\]\"](\"https:\/\/dpanagiotis.sites.sch.gr\/wp-content\/ql-cache\/quicklatex.com-53643324273c7a0da52e3f53217ef836_l3.png\" "\\"Rendered")
<\/p> ![\"\[-4x-7+1=x^2-9x\]\"](\"https:\/\/dpanagiotis.sites.sch.gr\/wp-content\/ql-cache\/quicklatex.com-c559bc6ff8da8477a22e36bfecd72dd3_l3.png\" "\\"Rendered")
<\/p><\/p>\n![\"\[0=x^2-9x+4x+7-1\Leftrightarrow\]\"](\"https:\/\/dpanagiotis.sites.sch.gr\/wp-content\/ql-cache\/quicklatex.com-119278ecd80300788068950f2527bf0f_l3.png\" "\\"Rendered")
<\/p> ![\"\[0=x^2-5x+6\]\"](\"https:\/\/dpanagiotis.sites.sch.gr\/wp-content\/ql-cache\/quicklatex.com-a57ef4d98710c141789804213cf32476_l3.png\" "\\"Rendered")
<\/p> \u03ae ![\"\[x^2-5x+6=0\]\"](\"https:\/\/dpanagiotis.sites.sch.gr\/wp-content\/ql-cache\/quicklatex.com-69d534862722701e5a75d9039ea6ebc5_l3.png\" "\\"Rendered")
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