Question

 

Answer 1

`@` `\text {Ans}`

`\downarrow`

`i)`

`1/7 < x/35 < 2/5`

`=> 5/35 < x/35 < 14/35`

`=> 5 < x < 14`

`=> x \in {6; 7; 8; ... 13}.`

`k)`

`5/13 < (2-x)/104 < 5/8`

`=> 40/104 < (2-x)/104 < 65/104`

`=> 40 < 2-x < 65`

`=> 2-x \in {41; 42; ... ; 64}`

`=> x \in {-39; -40; ... ; -62}.`

Answer 2

i) \(\dfrac{1}{7}< \dfrac{x}{35}< \dfrac{2}{5}\)

\(\Rightarrow\dfrac{5}{35}< \dfrac{x}{35}< \dfrac{14}{35}\)

\(\Rightarrow5< x< 14\)

\(\Rightarrow x\in\left\{6;7;8;9;10;11;12;13\right\}\)

k) \(\dfrac{5}{13}< \dfrac{2-x}{104}< \dfrac{5}{8}\)

\(\Rightarrow\dfrac{40}{104}< \dfrac{2-x}{104}< \dfrac{65}{104}\)

\(\Rightarrow40< 2-x< 65\)

\(\Rightarrow2-x\in\left\{41;42;43;...;64\right\}\)

\(\Rightarrow x\in\left\{-39;-40;...;-62\right\}\)

Answer 3

i: =>5/35<x/35<14/35

=>5<x<14

=>\(x\in\left\{6;7;8;9;10;11;12;13\right\}\)

k: =>\(\dfrac{40}{104}< \dfrac{2-x}{104}< \dfrac{65}{104}\)
=>\(40< 2-x< 65\)

=>\(2-x\in\left\{41;42;...;64\right\}\)

=>\(x\in\left\{-39;-40;...;-61;-62\right\}\)