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Question
Solve 2|x + 1| − 6 ≤ 7 and graph the solution set in a number line
Solution
2|x + 1| − 6 ≤ 7
⇒ 2|x + 1| ≤ 7 + 6 (= 13)
⇒ |x + 1| ≤ `13/2`
⇒ `x + 1 > (-13)/2`
or
`x + 1 < 13/2``
`x + 1 > (-13)/2`
⇒ `x > (-13)/2 - 1 (= (-15)/2)` ......(1)
`x + 1< 13/2`
⇒ `x < 13/2 - 1 (= 11/2)` .....(2)
From (1) and (2)
`(-15)/2 ≤ x ≤ 11/2`
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