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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
`-x/(3) ≤ x/(2) - 1(1)/(3) < (1)/(6), x ∈ "R"`
`-x/(3) ≤ x/(2) -1(1)/(3)`
`-x/(3) ≤ x/(2) - (4)/(3)`
`(4)/(3) ≤ x/(2) + x/(3)`
`(4)/(3) ≤ (5x)/(6)`
`(6)/(5) xx (4)/(3) ≤ x`
`(8)/(5) ≤ x`
`x/(2) -1(1)/(3) < (1)/(6)`
`x/(2) < (1)/(6) + (4)/(3)`
`x/(2) < (1 + 8)/(6)`
`x < (9 xx 2)/(6)`
x < 3
From (1) and (2)
`(8)/(5) ≤ x < 3`
or 1.6 ≤ x < 3
∴ Solution set {x : 1.6 ≤ x < 3, x ∈ R}
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