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प्रश्न
Solve the following inequation and graph the solution on the number line. `-2(2)/(3) ≤ x + (1)/(3) < 3 + (1)/(3)`x∈R
उत्तर
Given `-2(2)/(3) ≤ x + (1)/(3) < 3 + (1)/(3)` x∈R
`- (8)/(3) ≤ x + (1)/(3) < (10)/(3)`
Multiplying by 3, L.C.M. of fractions, we get
-8 ≤ 3x + 1 < 10
-8 - 1 ≤ 3x + 1 - 1 < 10 - 1 ...[Add - 1]
-9 ≤ 3x < 9
-3 ≤ x < 3 ...[Dividing by 3]
Hence the solution set is {x : x ∈ R, - 3 ≤ x < 3}
The graph of the solution set is shown by the thick portion of the number line. The solid circle at -3 indicates that the number -3 is included among the solutions where as the open circle at 3 indicates that 3 is not included among the solutions.
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