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प्रश्न
Solve the following inequation and represent the solution set on a number line.
`-8 1/2 < -1/2 - 4x ≤ 7 1/2, x ∈ I`
उत्तर
`-8 1/2 < -1/2 - 4x <= 7 1/2, x ∈ I`
`-8 1/2<-1/2 - 4x`
⇒ `(-17)/2<-1/2 - 4"x"`
⇒ `(-17)/2+1/2 < 4"x"`
⇒ `(-17)/2 < (- 1 - 8x)/2`
⇒ – 17 < – 1 – 8x
⇒ + 8x < – 1 + 17
⇒ 8x < 16
⇒ x < 2
`-1/2 - 4x ≤ 7 1/2`
⇒ `-1/2 - 4x ≤ 15/2`
⇒ `-4x ≤ 15/2 + 1/2`
⇒ – 4x ≤ 8
⇒ x ≥ – 2
So,
– 2 ≤ x < 2
As, `x ∈ I`
x = {–2, –1, 0, 1}
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