Solve the following in equation and represent the solution set on the number line 3x/5 + 2 < x + 4 ≤ x/2 + 5,x€R

Solution:

Given, 3x/5 + 2 < x + 4 ≤ x/2 + 5, x € R

Consider 3x/5 + 2 < x + 4

3x/5 - x < 4 - 2

(3x - 5x)/ 5 < 2

-2x/5 < 2

Dividing above equation throughout by (-2), we get,

x/5 > -1

⇒ x > -5------->(1)

Now, consider x + 4 ≤ x/2+5

x - x/2 ≤ 5 - 4

(2x -x)/ 2 ≤ 1

x/2 ≤ 1

⇒x ≤ 2 ----(2)

∴ from (1) and (2) solution is -5 < x ≤ 2.

Solution on number line:

Solve the following in equation and represent the solution set on the number line 3x/5 + 2 < x + 4 ≤ x/2 + 5,x€R

Summary: 

The solution for the equation 3x/5+ 2 < x + 4 ≤ x/2+5, x€R, is -5 < x ≤ 2.