Q13 of 122 Page 15

Solve each of the following system of equations in R.

Subtracting 9 from both sides, we get–

|3–4x|–9≥0

For this, we have 2 cases,

Case 1:

For this, |3–4x|=3–4x

3–4x–9≥0

–4x–6≥0

4x≤–6

…(1)

Case 2: 0<x<∞

For this, |3–4x|=–(3–4x)

–3+4x–9≥0

4x–12≥0

4x≥12

⇒ x≥3

⇒ xϵ [3, ∞ ) …(2)

(from 1 and 2)

We can verify the answers using graph as well.

Solve each of the following system of equations in R.

Find all pairs of consecutive odd positive integers, both of which are smaller than 10, such that their sum is more than 11.

Find all pairs of consecutive odd natural number, both of which are larger than 10, such that their sum is less than 40.