Question

Solve 2|x + 1| − 6 ≤ 7 and graph the solution set in a number line

Answer 1

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`