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प्रश्न
Solve the inequation and represent the solution set on the number line. `-3 + x ≤ (8x)/(3) + 2 ≤ (14)/(3) + 2x, "Where" x ∈ "I"`
उत्तर
Given: `-3 + x ≤ (8x)/(3) + 2 ≤ (14)/(3) + 2x, "Where" x ∈ "I"`
(i) `-3 + x ≤ (8x)/(3) + 2`
`-3 - 2 ≤ (8x)/(3) - x`
⇒ `-5 ≤ (5x)/(3)`
⇒ `-1 ≤ x/(3)`
–3 ≤ x ....(i)
and
`(8x)/(3) - 2x ≤ (14)/(3)`
⇒ `(2x)/(3) ≤ (8)/(3)`
⇒ x ≤ 4 ....(ii)
From (i) and (ii),
⇒ `-5 ≤ (5x)/(3) and (2x)/(3) ≤ (8)/(3)`
⇒ x ≥ –3 and x ≤ 4
∴ –3 ≤ x ≤ 4
Solution set = {–3, -2, –1, 0, 1, 2, 3, 4}
Solution set on number line
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