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

Expert Answers
sciencesolve eNotes educator| Certified Educator

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/` .

jaksonme91 | Student

There would be multiple answers to that problem, since it is an absolute value expression.

First, you remove the absolute value signs, and make two problems.

1: 2x-5>1

2: 2x-5 >-1

 

Then you solve each problem:

1st problem:

2x-5>1

2x>6

x>3

 

2nd problem:

2x-5>-1

2x>4

x>2

 

The answer is in an OR format. X is greater than 3, or X is greater than 2.

 

 

 

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