How would I solve this equation?  |2x-5|>1

Expert Answers

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You should use the absolute value property such that:

`|x|< a => -a < x < a`

`-1>2x-5>1 `

You need to solve the inequality `2x-5<-1`  such that:

`2x - 5<-1 => 2x < 5-1 => 2x<4 => x< 2`

`x in (-oo,2)`

You need to solve the inequality `2x-5>1`  such that:

`2x-5>1 => 2x>5+1 =>2x>6 => x>3`

`x in (3,oo)`

You should intersect the intervals above such that:

`x in (-oo,2)nn(3,oo)`  = `O/ `

Hence, evaluating the solution to the given inequality yields x in `(-oo,2)nn(3,oo)`  = `` `O/` .

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