Solve the system of equations in R.|(3x – 4)/2| ≤ 5/12

1.	Solve the system of equations in R.\|(3x – 4)/2\| ≤ 5/12
Answer» Given as \|(3x – 4)/2\| ≤ 5/12 Now, we can rewrite it as \|3x/2 – 4/2\| ≤ 5/12 \|3x/2 – 2\| ≤ 5/12 Suppose ‘r’ be a positive real number and ‘a’ be a fixed real number. Now, \|x – a\| ≤ r ⟺ a – r ≤ x ≤ a + r Here, a = 2 and r = 5/12 2 – 5/12 ≤ 3x/2 ≤ 2 + 5/12 (24 - 5)/12 ≤ 3x/2 ≤ (24 + 5)/12 19/12 ≤ 3x/2 ≤ 29/12 Then, multiplying the whole inequality by 2 and dividing by 3, we get 19/18 ≤ x ≤ 29/18 ∴ x ∈ [19/18, 29/18]

Answer»

Given as

|(3x – 4)/2| ≤ 5/12

Now, we can rewrite it as

|3x/2 – 4/2| ≤ 5/12

|3x/2 – 2| ≤ 5/12

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

|x – a| ≤ r ⟺ a – r ≤ x ≤ a + r

Here, a = 2 and r = 5/12

2 – 5/12 ≤ 3x/2 ≤ 2 + 5/12

(24 - 5)/12 ≤ 3x/2 ≤ (24 + 5)/12

19/12 ≤ 3x/2 ≤ 29/12

Then, multiplying the whole inequality by 2 and dividing by 3, we get

19/18 ≤ x ≤ 29/18

∴ x ∈ [19/18, 29/18]

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