Question

solve |(3x-4)÷2|<5/12​

Answer 1

Step-by-step explanation:

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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Answer 2

Answer:

Please See Downward

Step-by-step explanation:

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]Read more on Sarthaks.com - https://www.sarthaks.com/799607/solve-the-system-of-equations-in-r-3x-4-2-5-12

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