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Question
If x ∈ I, then the solution set of the inequation 1 < 3x + 5 ≤ 11 is
Options
{ – 1, 0, 1, 2}
{ – 2, – 1, 0, 1}
{ – 1, 0, 1}
`{x : x ∈ "R", -(4)/(3) < x ≤ 2}`
Solution
x ∈ I
1 < 3x + 5 ≤ 11
⇒ 1 < 3x + 5
⇒ 1 – 5 < 3x
⇒ –4 < 3x
⇒ `(-4)/(3) < x`
and
3 + 5 ≤ 11
⇒ 3x ≤ 11 – 5
⇒ 3x ≤ 6
⇒ `x ≤ (6)/(3)`
⇒ x ≤ 2
∴ `(-4)/(3) < x ≤ 2`
Solution set = {–1, 0, 1, 2}.
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