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Question
Solve the following inequation, write the solution set and represent it on the number line `-x/3 <= x/2 - 1 1/3 < 1/6, x ∈ R`
Solution
The given inequation is `-1/3 <= x/2 - 1 1/3 < 1/6, x ∈ R`
`-x/3 <= x/2 - 1 1/3`
`x/3 - x/2 <= -4/3`
`(2x + 3x)/6 >= 4/3`
`(5x)/6 >= 4/3`
`5x >= 8`
`x >= 8`
`x >= 8/5`
`x >= 1.6`
and
`x/2 - 1 1/3 < 1/6`
`x/2 < 1/6 + 4/3`
`x/2 < (1+8)/6`
`x/2 < 9/6`
`x < 18/6`
x < 3
The solution set is `{x: 1.6 <= x < 3, x ∈ R}`
It can be represented on a number line as follows:
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