Question

Solve for x: −6 < x − 1 < 9

5 < x < 10
−5 < x < 10
−5 > x > 10
5 > x > −10

Answer 1

`-5<x<10`

Explanation:

`-6<x-1<9`

If
`a<u<b\:` than
`a<u` and
`u<b`

`-6<x-1`

⇒ Switch sides:-

`x-1>-6`

⇒ Add 1 to both sides:-

`x-1+1>-6+1`

`x>-5`

And...

`\:x-1<9`

⇒ Add 1 to both sides:-

`x-1+1<9+1`

`x<10`

⇒ Now, Combine the intervals:-

`-5<x<10`

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