{"segment":[{"time":24,"part":[{"title":"Ch\u1ecdn k\u00ed hi\u1ec7u th\u00edch h\u1ee3p \u0111i\u1ec1n v\u00e0o \u00f4 tr\u1ed1ng","title_trans":"M\u1ed7i k\u00ed t\u1ef1 ch\u1ec9 \u0111i\u1ec1n \u0111\u01b0\u1ee3c v\u00e0o m\u1ed9t \u00f4 tr\u1ed1ng","correct":[["$\\notin$"],["$\\in$"],["$\\subset$"]],"temp":"drop_blank","list":[{"point":5,"word":["$\\in$","$\\subset$","$\\notin$"],"ques":" \u0110i\u1ec1n k\u00ed hi\u1ec7u th\u00edch h\u1ee3p ($\\in; \\notin; \\subset$) v\u00e0o \u00f4 tr\u1ed1ng <br\/> <p>$2\\dfrac{1}{2}$ _dr_blank_ Z; $\\qquad -1,5 $_dr_blank_ Q; $\\qquad $ Z _dr_blank_ Q<\/p>","explain":" Ta c\u00f3: $2\\dfrac{1}{2} = \\dfrac{5}{2} \\notin Z ; $$\\qquad -1,5 = \\dfrac{-3}{2} \\in Q ;$$\\qquad Z \\subset Q$ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c k\u00ed hi\u1ec7u ph\u1ea3i \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 $\\notin; \\in; \\subset $<\/span> "}]}],"id_ques":21},{"time":9,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u (>; <; =) th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng ","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" $\\dfrac{-7}{22} $_input_$ \\dfrac{-3}{8}$","hint":" So s\u00e1nh b\u1eafc c\u1ea7u v\u1edbi $\\dfrac{-7}{21} $ ; ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> So s\u00e1nh c\u00e1c s\u1ed1 h\u1eefu t\u1ec9<\/b> <br\/> $\\bullet$ D\u00f9ng t\u00ednh ch\u1ea5t b\u1eafc c\u1ea7u <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span> \\begin{align*} \\text{ Ta c\u00f3: } &\\dfrac{-7}{22} > \\dfrac{-7}{21} = \\dfrac{-1}{3} = \\dfrac{-3}{9} > \\dfrac{-3}{8} \\\\ &\\Rightarrow \\dfrac{-7}{22} > \\dfrac{-3}{8} \\end{align*} <br\/> <span class='basic_pink'> D\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 ''>''. <\/span><\/span> "}]}],"id_ques":22},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":" Trong t\u1eadp c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 $\\mathbb{Q},$ ph\u00e1t bi\u1ec3u n\u00e0o sau \u0111\u00e2y l\u00e0 \u0111\u00fang? ","select":["A. M\u1ecdi s\u1ed1 h\u1eefu t\u1ec9 \u0111\u1ec1u l\u1edbn h\u01a1n 0.","B. M\u1ecdi s\u1ed1 h\u1eefu t\u1ec9 \u0111\u1ec1u nh\u1ecf h\u01a1n 0.","C. Ch\u1ec9 c\u00f3 s\u1ed1 h\u1eefu t\u1ec9 \u00e2m l\u00e0 nh\u1ecf h\u01a1n 0.","D. Ch\u1ec9 c\u00f3 s\u1ed1 0 kh\u00f4ng ph\u1ea3i l\u00e0 s\u1ed1 h\u1eefu t\u1ec9."],"hint":" S\u1ed1 h\u1eefu t\u1ec9 bao g\u1ed3m : s\u1ed1 h\u1eefu t\u1ec9 \u00e2m, s\u1ed1 0 v\u00e0 s\u1ed1 h\u1eefu t\u1ec9 d\u01b0\u01a1ng.","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> S\u1ed1 h\u1eefu t\u1ec9 \u00e2m, d\u01b0\u01a1ng <\/b> <br\/> $ x > 0 \\Leftrightarrow x$ l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 d\u01b0\u01a1ng <br\/> $ x < 0 \\Leftrightarrow x$ l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 \u00e2m <br\/> S\u1ed1 h\u1eefu t\u1ec9 0 kh\u00f4ng l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 d\u01b0\u01a1ng c\u0169ng kh\u00f4ng l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 \u00e2m <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ph\u00e1t bi\u1ec3u \u0111\u00fang l\u00e0: <br\/> C. Ch\u1ec9 c\u00f3 s\u1ed1 h\u1eefu t\u1ec9 \u00e2m l\u00e0 nh\u1ecf h\u01a1n 0. <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span> ","column":2}]}],"id_ques":23},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" <center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai1/lv2/img\/4.jpg' \/><\/center> C\u00e1c s\u1ed1: $ 2; -0,2; 0; 2\\dfrac{1}{3} $ l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 \u0111\u00fang hay sai?","select":["A. \u0110\u00fang","B. Sai "],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b> \u0110\u1ecbnh ngh\u0129a <\/b> <br\/> S\u1ed1 h\u1eefu t\u1ec9 l\u00e0 s\u1ed1 \u0111\u01b0\u1ee3c vi\u1ebft d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1 $\\dfrac{a}{b}$ v\u1edbi $a,b \u2208 \\mathbb{Z} , b \u2260 0$. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $2 = \\dfrac{2}{1} \\\\ -0,2 = \\dfrac{-2}{10} \\\\ 2\\dfrac{1}{3} = \\dfrac{7}{3}$ <br\/> C\u00e1c s\u1ed1 tr\u00ean \u0111\u1ec1u bi\u1ec3u di\u1ec5n \u0111\u01b0\u1ee3c d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1 $\\dfrac{a}{b}$ n\u00ean n\u00f3 l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 <br\/> 0 l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n l\u00e0 \u0110\u00fang. <\/span><\/span> ","column":2}]}],"id_ques":24},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" Trong c\u00e1c ph\u00e2n s\u1ed1 sau : $ \\dfrac{-12}{15};\\dfrac{-15}{20};\\dfrac{-20}{28} .$ Ph\u00e2n s\u1ed1 n\u00e0o bi\u1ec3u di\u1ec5n s\u1ed1 h\u1eefu t\u1ec9 $\\dfrac{3}{-4}?$ ","select":[" A. $\\dfrac{-12}{15}$ "," B. $\\dfrac{-15}{20}$ "," C. $\\dfrac{-20}{28}$ "],"hint":" R\u00fat g\u1ecdn ph\u00e2n s\u1ed1 v\u1ec1 d\u1ea1ng t\u1ed1i gi\u1ea3n r\u1ed3i so s\u00e1nh v\u1edbi $\\dfrac{3}{-4}$","explain":" \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u01a1 b\u1ea3n c\u1ee7a ph\u00e2n s\u1ed1, ta c\u00f3: \\begin{align*} &\\dfrac{-12}{15} = \\dfrac{-4.3}{5.3} = \\dfrac{-4}{5} \\\\ &\\dfrac{-15}{20}= \\dfrac{3.(-5)}{-4.(-5)} = \\dfrac{-3}{4} = \\dfrac{3}{-4} \\\\ &\\dfrac{-20}{28} = \\dfrac{-5.4}{7.4} = \\dfrac{-5}{7} \\\\ &\\text { V\u1eady ph\u00e2n s\u1ed1 bi\u1ec3u di\u1ec5n s\u1ed1 h\u1eefu t\u1ec9 } \\dfrac{3}{-4} \\text { l\u00e0} : \\dfrac{-15}{20} \\end{align*} <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":3}]}],"id_ques":25},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":"<center><img src='https://www.luyenthi123.com/file/luyenthi123/lop7/toan/daiso/bai1/lv2/img\/4.jpg' \/><\/center> Ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang","select":["A. $ \\mathbb{Z} \\subset \\mathbb{N} \\subset \\mathbb{Q} $ ","B. $ \\mathbb{N} \\subset \\mathbb{Z} \\subset \\mathbb{Q} $ ","C. $ \\mathbb{N} \\subset \\mathbb{Q} \\subset \\mathbb{Z} $ ","D. $ \\mathbb{Q} \\subset \\mathbb{N} \\subset \\mathbb{Z} $ "],"explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> <b>Ta c\u00f3 \u0111\u1ecbnh ngh\u0129a: <\/b> <br\/> $ \\bullet \\quad \\mathbb{N}$ k\u00ed hi\u1ec7u t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 t\u1ef1 nhi\u00ean, bao g\u1ed3m $ 0 ; 1 ; 2 ; 3 ; \u2026 $ <br\/> $ \\bullet \\quad \\mathbb{Z}$ k\u00ed hi\u1ec7u t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 nguy\u00ean, bao g\u1ed3m $\u2026,-2 ;-1 ;0 ;1 ;2 ;\u2026$ <br\/> $\\bullet \\quad \\mathbb{Q}$ k\u00ed hi\u1ec7u t\u1eadp h\u1ee3p c\u00e1c s\u1ed1 h\u1eefu t\u1ec9, l\u00e0 s\u1ed1 \u0111\u01b0\u1ee3c vi\u1ebft d\u01b0\u1edbi d\u1ea1ng ph\u00e2n s\u1ed1 $\\dfrac{a}{b}$ v\u1edbi $a,b \u2208 \\mathbb{Z} , b \u2260 0$. <br\/> $\\bullet$ Ta c\u00f3 $ \\mathbb{N} \\subset \\mathbb{Z} \\subset \\mathbb{Q}$ <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Theo \u0111\u1ecbnh ngh\u0129a ta c\u00f3: $ \\mathbb{N} \\subset \\mathbb{Z} \\subset \\mathbb{Q} $ <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":26},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" C\u00e1c s\u1ed1 h\u1eefu t\u1ec9 $ \\dfrac{3}{4}; \\dfrac{-6}{-8}; \\dfrac{75}{100} $ \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1edfi m\u1ea5y \u0111i\u1ec3m tr\u00ean tr\u1ee5c s\u1ed1 ?","select":[" A. 1"," B. 2"," C. 3"," D. 4"],"explain":" \\begin{align*} \\text{ Ta c\u00f3: } &\\dfrac{-6}{-8} = \\dfrac{3.(-2)}{4.(-2)} = \\dfrac{3}{4} \\\\ &\\dfrac{75}{100} = \\dfrac{3.25}{4.25} = \\dfrac{3}{4} \\\\ &\\text{ Suy ra: } \\dfrac{3}{4} = \\dfrac{-6}{-8} = \\dfrac{75}{100} \\end{align*} V\u1eady c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 tr\u00ean \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1edfi m\u1ed9t \u0111i\u1ec3m tr\u00ean tr\u1ee5c s\u1ed1. <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":2}]}],"id_ques":27},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" C\u00e1c s\u1ed1 nguy\u00ean x, y th\u1ecfa m\u00e3n $\\dfrac{x}{2} = \\dfrac{3}{y}$ l\u00e0 : ","select":["A. $ x= 2; y = -3$","B. $x = 1 ; y = 6$"],"hint":" Thay x, y v\u00e0o bi\u1ec3u th\u1ee9c $ \\dfrac{x}{2} = \\dfrac{y}{3}$ r\u1ed3i so s\u00e1nh.","explain":" A. Thay $ x = 2; y = -3$ v\u00e0o $\\dfrac{x}{2} = \\dfrac{3}{y}$ c\u00f3 <br\/> $\\dfrac{2}{2} = 1 \\neq \\dfrac{3}{-3} = -1$ <br\/> B. Thay $ x = 1; y = 6$ v\u00e0o $\\dfrac{x}{2} = \\dfrac{3}{y}$ c\u00f3 <br\/> $\\dfrac{1}{2} = \\dfrac{3}{6} = \\dfrac{1}{2}$ <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":28},{"time":9,"part":[{"title":"\u0110i\u1ec1n d\u1ea5u th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng ( < ; = ; > )","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" $\\dfrac{2}{-7} $_input_$ \\dfrac{4}{-9} $","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> - Quy \u0111\u1ed3ng t\u1eed s\u1ed1 r\u1ed3i so s\u00e1nh m\u1eabu s\u1ed1. <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $ \\dfrac{2}{-7} = \\dfrac{4}{-14} $ <br\/> V\u00ec $ -14 < -9$ n\u00ean $ \\dfrac{4}{-14} > \\dfrac{4}{-9} $ hay $ \\dfrac{2}{-7} > \\dfrac{4}{-9} $ <br\/> <br\/> <span class='basic_pink'> D\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 ''>'' <\/span><\/span> "}]}],"id_ques":29},{"time":24,"part":[{"title":"\u0110i\u1ec1n k\u00ed t\u1ef1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng ( < ; = ; > )","title_trans":"","temp":"fill_the_blank","correct":[[[">"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" So s\u00e1nh c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 $\\dfrac{-4}{27} $_input_$ \\dfrac{10}{-63}$","hint":" Quy \u0111\u1ed3ng m\u1eabu r\u1ed3i so s\u00e1nh","explain":" Ta c\u00f3: $\\dfrac{-4}{27} = \\dfrac{-28}{189};$ $\\dfrac{10}{-63} = \\dfrac{-10}{63} = \\dfrac{-30}{189}$ <br\/> V\u00ec $\\dfrac{-28}{189} > \\dfrac{-30}{189}$ n\u00ean $\\dfrac{-4}{27} > \\dfrac{10}{-63}$ <br\/> <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n c\u1ea7n \u0111i\u1ec1n l\u00e0 ''>'' <\/span><\/span> "}]}],"id_ques":30},{"time":9,"part":[{"title":"\u0110i\u1ec1n k\u00ed t\u1ef1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng ( < ; = ; > )","title_trans":"","temp":"fill_the_blank","correct":[[["<"],[">"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" $\\dfrac{23}{-15} $_input_$ \\dfrac{-17}{-50};\\dfrac{127}{-128}$_input_$\\dfrac{-1345}{1344}$","hint":" C\u1eb7p \u0111\u1ea7u ti\u00ean so s\u00e1nh v\u1edbi 0; c\u1eb7p th\u1ee9 hai so s\u00e1nh v\u1edbi $-1$ ","explain":" \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u01a1 b\u1ea3n c\u1ee7a ph\u00e2n s\u1ed1 ta c\u00f3: \\begin{align*} &\\dfrac{23}{-15} < 0 < \\dfrac{-17}{-50} = \\dfrac{17}{50} \\Rightarrow \\dfrac{23}{-15} < \\dfrac{-17}{-50} \\\\ &\\dfrac{127}{-128} > -1 > \\dfrac{-1345}{1344} \\Rightarrow \\dfrac{127}{-128} > \\dfrac{-1345}{1344}\\end{align*} <br\/> <span class='basic_pink'> D\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u1ea7n l\u01b0\u1ee3t l\u00e0 ''<'' v\u00e0 ''>''. <\/span><\/span> "}]}],"id_ques":31},{"time":9,"part":[{"title":"\u0110i\u1ec1n k\u00ed t\u1ef1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng ( < ; = ; > )","title_trans":"","temp":"fill_the_blank","correct":[[["<"],[">"]]],"list":[{"point":5,"width":50,"type_input":"","ques":"$\\dfrac{2}{-7} $_input_$ \\dfrac{-3}{11}; \\dfrac{-213}{300} $_input_$ \\dfrac{18}{-25}$","hint":" Quy \u0111\u1ed3ng m\u1eabu s\u1ed1 r\u1ed3i so s\u00e1nh: ","explain":" <span class='basic_left'> \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u01a1 b\u1ea3n c\u1ee7a ph\u00e2n s\u1ed1 ta c\u00f3: <br\/> $\\bullet \\dfrac{2}{-7} = \\dfrac{-2}{7} = \\dfrac{-2.11}{7.11} = \\dfrac{-22}{77}; \\qquad \\dfrac{-3}{11}= \\dfrac{-3.7}{11.7} = \\dfrac{-21}{77}$ <br\/> Do $-22 < -21 \\Rightarrow$ $ \\dfrac{-22}{77} < \\dfrac{-21}{77} \\Rightarrow \\dfrac{2}{-7} < \\dfrac{-3}{11}$ <br\/> $\\bullet\\dfrac{-213}{300}; \\qquad \\dfrac{18}{-25} = \\dfrac{-18.12}{25.12} =\\dfrac{-216}{300}.$ <br\/> Do $ -213 > -216$ n\u00ean $ \\dfrac{-213}{300} > \\dfrac{-216}{300} \\Rightarrow \\dfrac{-213}{300} > \\dfrac{18}{-25}$ <br\/> <br\/> <span class='basic_pink'> D\u1ea5u c\u1ea7n \u0111i\u1ec1n l\u00e0 ''<'' v\u00e0 ''>''. <\/span><\/span> "}]}],"id_ques":32},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":" Cho c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 sau: $ x = \\dfrac{-12}{30}; y = \\dfrac{-3}{-7}; z = \\dfrac{10}{-25}$ <br\/> Kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang l\u00e0: ","select":[" A. $ x > y $ "," B. $ y < z $"," C. $ x = z $","D. $ z > x $"],"hint":" Quy \u0111\u1ed3ng m\u1eabu s\u1ed1 c\u00e1c ph\u00e2n s\u1ed1 r\u1ed3i so s\u00e1nh.","explain":" Ta c\u00f3: $x = \\dfrac{-12}{30} = \\dfrac{-2.6}{5.6} = \\dfrac{-2}{5}$ <br\/> $y = \\dfrac{-3}{-7} = \\dfrac{3}{7} > \\dfrac{-2}{5}$ <br\/> $z = \\dfrac{10}{-25} = \\dfrac{-10}{25} = \\dfrac{-2.5}{5.5} = \\dfrac{-2}{5}$ <br\/> Suy ra ta c\u00f3: $x = z < y $<br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span> ","column":2}]}],"id_ques":33},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" S\u1eafp x\u1ebfp c\u00e1c s\u1ed1 h\u1eefu t\u1ec9 sau theo th\u1ee9 t\u1ef1 t\u0103ng d\u1ea7n: $ \\dfrac{-18}{19}; \\dfrac{-2017}{2016}; \\dfrac{1990}{1988} $ ","select":[" A. $\\dfrac{-18}{19} < \\dfrac{-2017}{2016} < \\dfrac{1990}{1988} $ "," B. $\\dfrac{-2017}{2016} < \\dfrac{-18}{19} < \\dfrac{1990}{1988}$ "],"hint":" So s\u00e1nh b\u1eafc c\u1ea7u v\u1edbi -1; 0 ","explain":" \u00c1p d\u1ee5ng t\u00ednh ch\u1ea5t c\u01a1 b\u1ea3n c\u1ee7a ph\u00e2n s\u1ed1 ta c\u00f3: <br\/> \\begin{align*} &\\dfrac{-2017}{2016} < -1 < \\dfrac{-18}{19} < 0 < \\dfrac{1990}{1988} \\\\ &\\text{Suy ra: } \\dfrac{-2017}{2016} < \\dfrac{-18}{19} < \\dfrac{1990}{1988} \\end{align*}<br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":34},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[1]],"list":[{"point":5,"ques":" cho s\u1ed1 h\u1eefu t\u1ec9 $ x = \\dfrac{a-5}{-7}$. V\u1edbi gi\u00e1 tr\u1ecb n\u00e0o c\u1ee7a $a$ th\u00ec $x$ l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 d\u01b0\u01a1ng ","select":[" A. $ a < 5$ "," B. $ a = 5$"," C. $ a > 5$"],"hint":" S\u1ed1 h\u1eefu t\u1ec9 $\\dfrac{a}{b}$ l\u00e0 s\u1ed1 d\u01b0\u01a1ng n\u1ebfu $a$ v\u00e0 $b$ c\u00f9ng d\u1ea5u.","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> $\\bullet$ S\u1ed1 h\u1eefu t\u1ec9 $\\dfrac{a}{b}$ l\u00e0 s\u1ed1 d\u01b0\u01a1ng n\u1ebfu $a$ v\u00e0 $ b$ c\u00f9ng d\u1ea5u; l\u00e0 s\u1ed1 \u00e2m n\u1ebfu $a$ v\u00e0 $ b$ kh\u00e1c d\u1ea5u; b\u1eb1ng $0$ n\u1ebfu $a$ b\u1eb1ng $0$ <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $x$ l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 d\u01b0\u01a1ng $\\Leftrightarrow$ $a-5$ v\u00e0 $-7$ c\u00f9ng d\u1ea5u <br\/> Suy ra $ a - 5 < 0 $ (v\u00ec $-7 < 0$) <br\/> $\\Leftrightarrow a < 5 $ (v\u00e0 $a \\in \\mathbb{Z}$) <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 A. <\/span><\/span> ","column":3}]}],"id_ques":35},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[3]],"list":[{"point":5,"ques":" Cho s\u1ed1 h\u1eefu t\u1ec9 $ x = \\dfrac{3m-12}{6}$ v\u1edbi $ m \\in \\mathbb{Z}.$ T\u00ecm gi\u00e1 tr\u1ecb c\u1ee7a $m$ \u0111\u1ec3 $x$ l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 \u00e2m. ","select":[" A. $ m > 4$ "," B. $ m = 4$"," C. $ m < 4$"],"hint":" S\u1ed1 h\u1eefu t\u1ec9 $\\dfrac{a}{b} $ l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 \u00e2m n\u1ebfu $a$ v\u00e0 $b$ tr\u00e1i d\u1ea5u. ","explain":" <span class='basic_left'><span class='basic_green'>H\u01b0\u1edbng d\u1eabn:<\/span> <br\/> $\\bullet$ S\u1ed1 h\u1eefu t\u1ec9 $\\dfrac{a}{b}$ l\u00e0 s\u1ed1 d\u01b0\u01a1ng n\u1ebfu $a$ v\u00e0 $ b$ c\u00f9ng d\u1ea5u; l\u00e0 s\u1ed1 \u00e2m n\u1ebfu $a$ v\u00e0 $ b$ kh\u00e1c d\u1ea5u; b\u1eb1ng $0$ n\u1ebfu $a$ b\u1eb1ng $0$ <\/span> <br\/> <br\/> <span class='basic_green'>B\u00e0i gi\u1ea3i:<\/span><br\/> Ta c\u00f3: $x$ l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 \u00e2m $\\Leftrightarrow$ $3m -12$ v\u00e0 $6$ tr\u00e1i d\u1ea5u <br\/> Suy ra $ 3m - 12 < 0 $ (v\u00ec $6 > 0$) <br\/> $\\Leftrightarrow 3m < 12 \\Leftrightarrow m < \\dfrac{12}{3} = 4$ (v\u00e0 $m \\in \\mathbb{Z}$) <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 C. <\/span><\/span> ","column":3}]}],"id_ques":36},{"time":9,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng ","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["6"],["7"],["8"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm $x \\in \\mathbb{Z}$ \u0111\u1ec3 $\\dfrac{x-5}{9-x}$ l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 d\u01b0\u01a1ng <br\/> (Vi\u1ebft k\u1ebft qu\u1ea3 t\u1eeb b\u00e9 \u0111\u1ebfn l\u1edbn) <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x$= _input_; _input_; _input_ ","hint":" Ph\u00e2n s\u1ed1 $\\dfrac{a}{b} $d\u01b0\u01a1ng n\u1ebfu a v\u00e0 b c\u00f9ng d\u1ea5u ","explain":" <span class='basic_left'> \u0110\u1ec3 ph\u00e2n s\u1ed1 $\\dfrac{x-5}{9-x}$ d\u01b0\u01a1ng th\u00ec <br\/> Tr\u01b0\u1eddng h\u1ee3p 1: $\\left\\{ \\begin{align}& x-5>0 \\\\ & 9-x>0 \\\\\\end{align} \\right.$$\\Leftrightarrow \\left\\{ \\begin{align} & x>5 \\\\ & x<9 \\\\ \\end{align} \\right.$$\\Rightarrow x\\in \\text{ }\\!\\!\\{\\!\\!\\text{ }6,7,8\\}$ <br\/> Tr\u01b0\u1eddng h\u1ee3p 2: $\\left\\{ \\begin{align} & x-5>9 \\\\ \\end{align} \\right.$$\\Rightarrow x\\in \\varnothing $ <br\/> <span class='basic_pink'> V\u1eady c\u00e1c s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $6; 7; 8$<\/span><\/span> "}]}],"id_ques":37},{"time":9,"part":[{"title":"\u0110i\u1ec1n s\u1ed1 th\u00edch h\u1ee3p v\u00e0o ch\u1ed7 tr\u1ed1ng ","title_trans":"\u0110\u1ec1 chung cho hai c\u00e2u","temp":"fill_the_blank","correct":[[["5"]]],"list":[{"point":5,"width":50,"type_input":"","ques":" T\u00ecm $x \\in \\mathbb{Z}$ \u0111\u1ec3 $\\dfrac{x-5}{9-x}$ kh\u00f4ng l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 \u00e2m c\u0169ng kh\u00f4ng l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 d\u01b0\u01a1ng <br\/> <b> \u0110\u00e1p s\u1ed1: <\/b> $x$= _input_","hint":" S\u1ed1 0 kh\u00f4ng l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 \u00e2m c\u0169ng kh\u00f4ng l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 d\u01b0\u01a1ng ","explain":" <span class='basic_left'> \u0110\u1ec3 ph\u00e2n s\u1ed1 $\\dfrac{x-5}{9-x}$ kh\u00f4ng l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 \u00e2m c\u0169ng kh\u00f4ng l\u00e0 s\u1ed1 h\u1eefu t\u1ec9 d\u01b0\u01a1ng <br\/> Suy ra $\\dfrac{x-5}{9-x} = 0 \\Leftrightarrow x - 5 = 0 \\Leftrightarrow x = 5$<br\/> <span class='basic_pink'> V\u1eady s\u1ed1 c\u1ea7n \u0111i\u1ec1n l\u00e0 $5$<\/span><\/span> "}]}],"id_ques":38},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" C\u00f3 bao nhi\u00eau s\u1ed1 h\u1eefu t\u1ec9 c\u00f3 d\u1ea1ng $\\dfrac{7}{a}$ bi\u1ebft r\u1eb1ng $\\dfrac{9}{13} < \\dfrac{7}{a} < \\dfrac{9}{11}$ ","select":[" A. 1"," B. 2"," C. 3"],"explain":" <span class='basic_left'> Ta c\u00f3: $\\dfrac{9}{13} < \\dfrac{7}{a} < \\dfrac{9}{11}$ <br\/> Quy \u0111\u1ed3ng t\u1eed s\u1ed1 ta \u0111\u01b0\u1ee3c: $\\dfrac{63}{91} < \\dfrac{63}{9a} < \\dfrac{63}{77} $ <br\/> $\\Rightarrow 91 > 9a > 77$$\\Rightarrow 10\\dfrac{1}{9} > a > 8\\dfrac{5}{9}$ <br\/> Do $a\\in \\mathbb{Z}$ n\u00ean ch\u1ecdn c\u00e1c gi\u00e1 tr\u1ecb $ 9; 10$ <br\/> Suy ra c\u00f3 2 s\u1ed1 h\u1eefu t\u1ec9 th\u1ecfa m\u00e3n \u0111\u1ec1 b\u00e0i <br\/> <span class='basic_pink'> V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B <\/span><\/span> ","column":3}]}],"id_ques":39},{"time":9,"part":[{"title":"L\u1ef1a ch\u1ecdn \u0111\u00e1p \u00e1n \u0111\u00fang nh\u1ea5t","title_trans":"","temp":"multiple_choice","correct":[[2]],"list":[{"point":5,"ques":" C\u00f3 bao nhi\u00eau ph\u00e2n s\u1ed1 c\u00f3 m\u1eabu s\u1ed1 b\u1eb1ng $7$, l\u1edbn h\u01a1n $\\dfrac{-5}{9}$ v\u00e0 nh\u1ecf h\u01a1n $\\dfrac{-2}{9}$ ","select":[" A. 1"," B. 2"," C. 3"," D. 4"],"hint":" Quy \u0111\u1ed3ng m\u1eabu s\u1ed1 c\u00e1c ph\u00e2n s\u1ed1 r\u1ed3i so s\u00e1nh. ","explain":" <span class='basic_left'> Do ph\u00e2n s\u1ed1 c\u00f3 m\u1eabu b\u1eb1ng 7 n\u00ean ph\u00e2n s\u1ed1 c\u1ea7n t\u00ecm c\u00f3 d\u1ea1ng $\\dfrac{x}{7}$ <br\/> Khi \u0111\u00f3, ta c\u00f3: $\\dfrac{-5}{9} < \\dfrac{x}{7} < \\dfrac{-2}{9}$ <br\/> Quy \u0111\u1ed3ng m\u1eabu ta \u0111\u01b0\u1ee3c: $ \\dfrac{-35}{63} < \\dfrac{9x}{63} < \\dfrac{-14}{63}$ <br\/> Suy ra $-35 < 9x < -14$$\\Rightarrow -3\\dfrac{8}{9} < x < -1\\dfrac{5}{9} $ <br\/> V\u00ec $ x \\in \\mathbb{Z}$ n\u00ean $ x \\in \\lbrace -2; -3 \\rbrace$ <br\/> V\u1eady ta c\u00f3 hai ph\u00e2n s\u1ed1 th\u1ecfa m\u00e3n $\\dfrac{-5}{9} < \\dfrac{x}{7} < \\dfrac{-2}{9}$ l\u00e0 : $\\dfrac{-3}{7} \\text{ v\u00e0} \\dfrac{-2}{7}$ <br\/> <span class='basic_pink'> \u0110\u00e1p \u00e1n \u0111\u00fang l\u00e0 B. <\/span><\/span> ","column":2}]}],"id_ques":40}],"lesson":{"save":0,"level":2}}