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" in "R"`

Answer 1

The given inequation is 

`-"x"/3≤ "x"/2 -1 1/3<1/6, "x" in "R"`

⇒ -`"x"/3 ≤ "x"/2 - 4/3 < 1/6`

Now,

`"x"/3 ≤ "x"/2 - 4/3`  ⇒ `-"x"/3 - "x"/2 ≤-4/3` ⇒ `(2"x" + 3"x")/6 ≥ 4/3` ⇒ `(5"x")/6 ≥ 4/3` ⇒ 5 x ≥ 8 ⇒ x ≥ `8/5` ⇒ x ≥ 1.6

`"x"/2 ≤ 4/3 - 1/6`  ⇒ `"x"/2 < 1/6 + 4/3`  ⇒ `"x"/2 < (1+4xx2)/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: