#### Question

Solve the following inequation and represent the solution set on the number line

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

#### Solution

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:

Is there an error in this question or solution?

Solution Solve the Following Inequation and Represent the Solution Set on the Number Line 4x - 19 < (3x)/5 - 2 <= (-2)/5 + X, X ∈ R Concept: Representation of Solution on the Number Line.