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

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

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's profile pic

jaksonme91 | Student, Undergraduate | (Level 1) eNoter

Posted on

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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