#### 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

The Given inequation is

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

`=> (4x - 19) < (3x - 10)/5 <= (-2 + 5x)/5`

`=> 5(4x - 19) < 3x - 10 < -2 + 5x`

`=> 20x - 95 < 3x - 10 <= -2 + 5x`

Solving `20x - 95 < 3x - 10`

`=> 17x < 85`

`=> x < 5`

Solving 3x - 10 <= -2 + 5x

`=> -2x <= 8`

`=> -x <= 4`

`=> x >= -4`

So the solution set = `{x : -4 <= x < 5, x in R}`

**Representation on the Number line**

Is there an error in this question or solution?

#### APPEARS IN

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.