Answer 1

Consider the given inequation

`4x - 19 < (3x)/5 - 2 <= (-2)/5 + x, x ∈ R`

`=> 4x - 19 + 2 < (3x)/5 - 2 + 2 <= (-2)/5 + x + 2, x ∈ R`

`=> 4x  - 17 < (3x)/5 <= x + 8/5, x ∈ R`

`=> 4x-(3x)/5<17  "and"  (-8)/5 <=x-(3x)/5,x ∈R `

`=> (20x  - 3x)/5 < 17 and (-8)/5 <= (5x - 3x)/5, x ∈ R`

`=> (17x)/5  <  17`  and `(-8)/5  <= (2x)/5, x ∈ R`

`=> x/5   < 1 and -4 <= x, x ∈ R`

`=> x < 5 and -4 <= x, x ∈ R`

=> -4 ≤ x < 5; where x ∊ R

 The solution set can be represented on a number line as follows: