Question

Find the solutions of the inequality.
|x-5|>3

Answer 1

I'll give you a start
x - 5 > 3 and x - 5 < -3

Answer 2

now you can easily find solutions for x

Answer 3

@Kanwar245 This is my first time taking algebra

Answer 4

@Kanwar245 when ya have absoulte value signs it turns pos. so therefore @Sevier it would be x+5>3 and x+5<-3

Answer 5

The absolute value encompassing (x-5) makes al the values inside positive. Since we're looking for all values greater than 3, we need to find all values that make (x-5)>3 and (x-5)<-3. Why are we looking for values (x-5)<-3? It is because any negatives smaller than -3 that are in an absolute value are made positive, and are therefore made larger than 3, which is what we are looking for.

Our answer should end up being a range of numbers. (-INFINITY, 2)(8, INFINITY) should be the answer. That means that all values from 8 to infinity, or from 2 to negative infinity, will yield a value greater than 3 for the equation |x-5|>3

*SIDENOTE* @beth89 While it is true that the absolute value turns the sign positive, it only turns the ENTIRE thing positive, not the signs within the function. For example: If we have |x-10| where x=2, we don't have |2+10|=12, what we DO get is |2-10|=|-8|=8
So basically, do whatever must be done within the absolute function as you normally would, then make the value positive.

Answer 6

So @Nitro-Nito the answer to the question find the solutions of the inequality is (-infinity,2)(8,infinity)

Answer 7

Yep!