1/3 + 3/35 < x/210 < 4/7 +3/5 +1/3
Ai thông minh giải giúp mình nha. Ahihi.
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\(\dfrac{1}{3}+\dfrac{3}{35}< \dfrac{x}{210}< \dfrac{4}{7}+\dfrac{1}{3}\)
Ta có: \(\dfrac{1}{3}+\dfrac{3}{35}=\dfrac{35+9}{105}=\dfrac{44}{105}\)
và \(\dfrac{4}{7}+\dfrac{1}{3}=\dfrac{12+7}{21}=\dfrac{19}{21}\)
=> \(\dfrac{44}{105}=\dfrac{44.2}{105.2}=\dfrac{88}{210}\)
=> \(\dfrac{19}{21}=\dfrac{19.10}{21.10}=\dfrac{190}{210}\)
=> \(\dfrac{88}{201}< \dfrac{x}{210}< \dfrac{190}{210}\)
=> Vậy x ∈ {89; 90; 91; 92; ... ; 188; 189}
2: =>3<x<16/5+9/5=5
=>x=4
1: =>70/210+18/210<x/210<120/210+70/210
=>88<x<190
hay \(x\in\left\{89;90;...;189\right\}\)
a: \(\dfrac{1}{3}+\dfrac{3}{35}< \dfrac{x}{210}< \dfrac{4}{7}+\dfrac{3}{5}+\dfrac{1}{2}\)
\(\Leftrightarrow\dfrac{70}{210}+\dfrac{18}{210}< \dfrac{x}{210}< \dfrac{120}{210}+\dfrac{126}{210}+\dfrac{105}{210}\)
\(\Leftrightarrow88< x< 441\)
b: Ta có: \(\dfrac{5}{3}+\dfrac{-14}{3}< x< \dfrac{8}{5}+\dfrac{18}{10}\)
\(\Leftrightarrow\dfrac{5}{3}-\dfrac{14}{3}< x< \dfrac{8}{5}+\dfrac{9}{5}\)
=>-9/3<x<17/5
=>-3<x<3,4
mà x là số nguyên
nên \(x\in\left\{-2;-1;0;1;2;3\right\}\)
\(\frac{1}{3}+\frac{3}{35}< \frac{x}{210}< \frac{4}{7}+\frac{3}{5}+\frac{1}{3}\)
\(\frac{44}{105}< \frac{x}{210}< \frac{158}{105}\)
\(\frac{88}{210}< \frac{x}{210}< \frac{316}{210}\)
suy ra x = { 89:90;91;............315}
1/3+3/35<x/210<4/7+3/5+1/3
=>44/105<x/210<158/105
=>88/210<x/210<316/210
=>x thuộc {89;90;91;92;...;313;314;315}
k nha bn