Solve the system of equations in R.|x + 1/3| > 8/3

1.	Solve the system of equations in R.\|x + 1/3\| > 8/3
Answer» Suppose ‘r’ be a positive real number and ‘a’ be a fixed real number. Now, \|x + a\| > r ⟺ x > r – a or x < – (a + r) Here, a = 1/3 and r = 8/3 x > 8/3 – 1/3 or x < – (8/3 + 1/3) x > (8 - 1)/3 or x < – (8 + 1)/3 x > 7/3 or x < – 9/3 x > 7/3 or x < – 3 x ∈ (7/3, ∞) or x ∈ (–∞, -3) ∴ x ∈ (–∞, -3) ∪ (7/3, ∞)

Answer»

Suppose ‘r’ be a positive real number and ‘a’ be a fixed real number. Now,

|x + a| > r ⟺ x > r – a or x < – (a + r)

Here, a = 1/3 and r = 8/3

x > 8/3 – 1/3 or x < – (8/3 + 1/3)

x > (8 - 1)/3 or x < – (8 + 1)/3

x > 7/3 or x < – 9/3

x > 7/3 or x < – 3

x ∈ (7/3, ∞) or x ∈ (–∞, -3)

∴ x ∈ (–∞, -3) ∪ (7/3, ∞)

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