Question

Just an absolute value question
|2x-3|>8 how is this equation solved to reflect the absolute value sign ?

Answer 1

Anytime you come across an inequality involving absolutes, split the problem into two inequalities with the absolute sign removed:

|2x - 3| > 8
+(2x - 3) > 8 OR
-(2x - 3) > 8

Solve the two inequalities separately and combine the solution.

Answer 2

typing out loud then \[x > \frac{ 11 }{ 2 } or .. x >-\frac{ 11 }{ 2}\] so it equals 5.5 or

-5.5 ?

Answer 3

2x - 3 < -8
2x < -5
x < - 5/2
you cant just change the sign...

Answer 4

I just5t looking at it again .....

Answer 5

I am stuck about the "you cant just change the sign " line along with making 8 negative 8 and going from > .... to <

Answer 6

+(2x - 3) > 8 OR
-(2x - 3) > 8

The first inequality +(2x - 3) > 8 gives:
2x > 11
x > 11/2

-(2x - 3) > 8
To get rid of the negative sign if we divide both sides by -1 we should flip the inequality meaning > will change to < or < will change to >
divide both sides by -1:
2x - 3 < - 8
add 3 to both sides
2x < -5
x < -5/2

The solution is x < -5/2 OR x > 11/2
You can leave the solution like that.

Or, if you have been taught interval notation, you can write the solution as:
(-infinity, -5/2) U (11/2, infinity) (where U is the union symbol).