Question

please please help me! |x-2|≥2x-1 thank you!
i'm so confused! :(

Answer 1

thank you for noticing my post, amistre64!

Answer 2

an absolute value can never be negative; so try to determine the right side of it according to 0 or positive results to narrow the odds

Answer 3

lol, thnks for posting it :)

Answer 4

2x-1 >= 0 is a good start

Answer 5

what do i do after x≥1/2 ? the answer is said to be x≤1 i'm really sorry. i'm so lost!! if the question just had an equal sign instead, i'd totally answer it but it isn't! :(

Answer 6

you work it just like it had an equal sign, and then adjust it in the end really

Answer 7

so we know x has to be greater than or equal to 1/2 so now solve it as tho it had an equals sign and get rid of all the values less than 1/2

Answer 8

|x-2|≥2x-1

hmmm, also; the right side appears to be able to go negative since the | | parts is always greater then a negative hmmm

Answer 9

-(x-2) >= 2x-1
(x-2) >= 2x-1

solve for both equations and we should be closer to an answer :)

Answer 10

Hey, @amistre64 @dydlf
might I suggest an alternative way?

Let's look at a simpler case for absolute value inequalities:
Suppose
|x| > 5
Then for sure, any value that satisfies
x > 5 would suffice, but is that the only way?
It can be shown that if
x < -5,
the inequality
|x| > 5 will still hold :)

Basically, the way to solve avi's (absolute value inequalities) such as this, is, as @amistre64 said, treat it as you would an equal sign (almost, lol, but more on that on request :D )

So, in general, if you have
|a| > b
then....
a > b
OR
a < -b (remove the absolute value sign, reverse inequality, negate the other side)

Our example here is just a fancier case :D

Answer 11

good information terez

Answer 12

thanks :)

Answer 13

-(x-2) >= 2x-1 ; distribute the - thru

-x+2 >= 2x-1 ; then solve as usual
+x+1 +x+1
--------------
3 >= 3x ; 1 >= x


(x-2) >= 2x-1 ; this is just a usual result, undo the ( ) and work it

x-2 >= 2x-1
-x+1 -x+1
-------------
-1 >= x

how we have 2 cases to chk

Answer 14

mark these results on a number line

Answer 15

since we have a "step" where they differ; test a value in that area to see if it works; if it does we are good. Id use 0 as a test

Answer 16

Don't we just take the union of the two sets? That way, since one is a subset of the other, the solution is just the superset?

Answer 17

if it was an = sign, maybe; but its good to test all areas to be certain

Answer 18

union means or doesnt it lol

Answer 19

i like dbl chking to be sure since i can never remember the fancier ways

Answer 20

Double checking never killed anyone, lol :D

Answer 21

solve these equations
+(x-2)>=2x-1;
-(x-2)>=2x-1;.....