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प्रश्न
Solve the inequation : `-2(1)/(2) + 2x ≤ (4x)/(3) ≤ (4)/(3) + 2x, x ∈ "W"`. Graph the solution set on the number line.
उत्तर
`-2(1)/(2) + 2x ≤ (4x)/(3) ≤ (4)/(3) + 2x, x ∈ "W"`
`-(5)/(2) + 2x ≤ (4x)/(3) ≤ (4)/(3) + 2x`
`-(5)/(2) + 2x ≤ (4x)/(3) and (4x)/(3) ≤ (4)/(3) + 2x`
`2x - (4x)/(3) ≤ (5)/(2) and (4x)/(3) - 2x ≤ (4)/(3)`
12 x - 8x ≤ 15 and 4x - 6x ≤ 4
4x ≤ 15 and -2x ≤ 4
`x ≤ (15)/(4) and -x ≤ 4`
`x ≤ (15)/(4) and x ≥ 4 `
`x ≤ (15)/(4) and -4 ≤ x `
∴ `-2 ≤ x ≤ (15)/(4)`
∴ x = 0, 1, 2, 3
Solution set {x : x ∈ W, x ≤ 3}
Solution set on number line
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