Question

Solve the following in equation write the solution set and represent it on the number line:

`-x/3 <= x/2 -1 1/3 < 1/6, x ∈ R`

Answer 1

The given inequation is

`x/3 <= x/2 -1 1/3 < 1/6` , x ∈ R

`=> -x/3 <= x/2 - 4/3 < 1/6`

Now

-x/3 <= x/2 - 4/3

`=> -x/3 -  x/2 <= -4/3`

`=> (2x + 3x)/6 >= 4/3`

`=> (5x)/6 >= 4/3`

`=> 5x >= 8`

`=> x >= 8/5`

`=> x >= 1.6`

`x/2 -  4/3 < 1/6`

`=> x/2 < 1/6 + 4/3`

`=> x/2  < (1 + 4 xx 2)/6`

`=>x/2 < (1 + 8)/6`

`=> x/2 < 9/6`

`=> x/2 < 3/2`

`=> x < 3`

∴ Solution set = {x : 1.6 <= x < 3}

It can be represented on a number line as follows