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Question
Find the values of x, which satisfy the inequation
`-2(5)/(6) <(1)/(2) - (2x)/(3) ≤ 2, x ∈ "W"`. Graph the solution set on the number line.
Solution
`-2(5)/(6) <(1)/(2) - (2x)/(3) ≤ 2`
Taking, `-2(5)/(6) <(1)/(2) - (2x)/(3)`
`-(17)/(6) < (1)/(2) - (2x)/(3)`
`-(17)/(6) - (1)/(2) < - (2x)/(3)`
`(-17 - 3)/(6) < -(2x)/(3)`
`-(20)/(6) < - (2x)/(3)`
⇒ `(10)/(3) > (2x)/(3)`
5 > x ...(1)
Now taking, `(1)/(2) - (2x)/(3) ≤ 2`
`-(2x)/(3) ≤ 2 -(1)/(2)`
`-(2x)/(3) ≤ (3)/(2)`
`-x ≤ (9)/(4)`
⇒ x ≥ - `(9)/(4)` ...(2)
From (1) and (2), we get
`-(9)/(4) ≤ x < 5`
⇒ `-2 (1)/(4) ≤ x < 5`
Required number line,
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