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a) \(\frac{1}{3}+\frac{3}{35}< \frac{x}{210}< \frac{7}{7}+\frac{3}{5}+\frac{1}{3}\)
\(\Rightarrow\frac{44}{105}< \frac{x}{210}< \frac{29}{15}\)
\(\Rightarrow\frac{88}{210}< \frac{x}{210}< \frac{406}{210}\)
\(\Rightarrow x\in\left\{89;90;91;...;405\right\}\)
b) \(\frac{5}{3}+-\frac{14}{3}< x< \frac{8}{5}+\frac{8}{10}\)
\(\Rightarrow-3< x< 2\frac{2}{5}\)
=> x thuộc {-2;-1;0;1;2} ( nếu x là số nguyên)
\(a)\frac{1}{3}+\frac{-2}{5}+\frac{1}{6}+\frac{-1}{5}\le x< \frac{-3}{4}+\frac{2}{7}+\frac{-1}{4}+\frac{3}{5}+\frac{5}{7}\)
\(\Rightarrow\frac{1}{3}+\frac{1}{6}+\frac{-2}{5}+\frac{-1}{5}\le x< \frac{-3}{4}+\frac{-1}{4}+\frac{2}{7}+\frac{5}{7}+\frac{3}{5}\)
\(\Rightarrow\frac{2}{6}+\frac{1}{6}+\frac{-3}{5}\le x< -1+1+\frac{3}{5}\)
\(\Rightarrow\frac{1}{2}+\frac{-3}{5}\le x< \frac{3}{5}\)
\(\Rightarrow\frac{-1}{10}\le x< \frac{6}{10}\)
\(\Rightarrow-1\le x< 6\)
\(\Rightarrow x\in\left\{-1;0;1;2;3;4;5\right\}\)
Bài b tương tự
\(b.\frac{1}{3}+\frac{3}{35}< \frac{x}{210}< \frac{4}{7}+\frac{3}{5}+\frac{1}{3}\)
\(\Leftrightarrow\frac{35+9}{105}< \frac{x}{210}< \frac{60+63+35}{105}\)
\(\Leftrightarrow\frac{44}{105}< \frac{x}{210}< \frac{158}{105}\)
\(\Leftrightarrow\frac{88}{210}< \frac{x}{210}< \frac{316}{210}\)
Suy ra \(x\in\left\{89;90;100;...;313;314;315\right\}\)
\(c.\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(\Leftrightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(\Leftrightarrow\frac{1}{11}-\frac{1}{21}-x+\frac{221}{231}=\frac{4}{3}\)
\(\Leftrightarrow\frac{21-11-231x+221}{231}=\frac{308}{231}\)
\(\Leftrightarrow-231x=308-21+11-221\)
\(\Leftrightarrow-231x=77\)
\(\Leftrightarrow x=-\frac{77}{231}=-\frac{1}{3}\)
^^
\(\frac{1}{3}+\frac{-2}{5}+\frac{1}{6}-\frac{1}{5}\le x< \frac{-3}{4}+\frac{2}{7}-\frac{1}{4}+\frac{3}{5}+\frac{5}{7}\)
\(=\frac{1.10}{3.10}+\frac{-2.6}{5.6}+\frac{1.5}{6.5}-\frac{1.6}{5.6}\le x< \frac{-3.35}{4.35}+\frac{2.20}{7.20}-\frac{1.35}{4.35}+\frac{3.28}{5.28}+\frac{5.20}{7.20}\)
\(=\)\(\frac{10}{30}+\frac{-12}{30}+\frac{5}{30}-\frac{6}{30}\le x< \frac{-105}{140}+\frac{40}{140}-\frac{35}{140}+\frac{84}{140}+\frac{100}{140}\)
\(=\)\(\frac{10+\left(-12\right)+5-6}{30}\le x< \frac{-105+40-35+84+100}{140}\)
\(=\)\(\frac{-3}{30}\le x< \frac{84}{140}\)
\(=\)\(\frac{-3.14}{30.14}\le x< \frac{84.3}{140.3}\)
\(=\)\(\frac{-42}{420}\le x< \frac{252}{420}\)
\(\Rightarrow-42\le x< 252\)
\(\Rightarrow x=\left\{-42;-41;-41;...;249;250;251;252\right\}\)
Chúc bạn một buổi chiều vui vẻ ~! ❤‿❤
Nếu có sai gì thì báo lỗi với mình nhé!
Cái bước thứ hai từ dưới lên sai rồi nhé em! KHông đc vứt mẫu số như vậy :)
Có 1/3+3/35=44/105
Có 4/7+3/5+1/3=158/105
=> 44/105< x/210<158/105 MC: 210
=> 88/210< x/210< 316/210
Vậy x thuộc {89;90;91;92;...;315}
Ta có :
\(\frac{1}{3}+\frac{3}{35}< \frac{x}{210}< \frac{4}{7}+\frac{3}{5}+\frac{1}{3}\)
\(\Leftrightarrow\)\(\frac{70}{210}+\frac{18}{210}< \frac{x}{210}< \frac{120}{210}+\frac{126}{210}+\frac{70}{210}\)
\(\Leftrightarrow\)\(\frac{70+18}{210}< \frac{x}{210}< \frac{120+126+70}{210}\)
\(\Leftrightarrow\)\(\frac{88}{210}< \frac{x}{210}< \frac{316}{210}\)
\(\Leftrightarrow\)\(88< x< 316\)
\(\Rightarrow\)\(x\in\left\{89;90;91;...;314;315\right\}\)
Vậy \(x\in\left\{89;90;91;...;314;315\right\}\)
Chúc bạn học tốt ~