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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"`
Solution
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:
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