Question

Solve the following inequation and graph the solution on the number line. `-2(2)/(3) ≤ x + (1)/(3) < 3 + (1)/(3)`x∈R

Answer 1

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.