Graph, on the number line, all points for which?

Question

|x-4|>2

Can some one show me how to do this problem.

Answer 1

ok, because of the absolute value marks, you actually have 2 equasions:

x-4>2
and
-(x-4)>2

solve each one individually:

x-4>2
+4 = +4 add 4
x>6 plot this

-(x-4)>2
*-1 = *-1 multiply by -1
x+4<-2
-4 = -4 subtract 4
x<-6 plot this also

hope this helps you out

Answer 2

Well, if |x-4|>2, then:
EITHER
(x-4)>2
OR
(x-4)<-2

If it is the first one [ (x-4)>2 ], then (by adding 4 to each side of the equation), we have:
x>6

If it is the second one [ (x-4)<-2 ], then (by adding 4 to each side of the equation again), we have:
x<2

So the inequality will be satisfied if x is either greater than 6 or less than 2. In other words, anything on the number line works EXCEPT the numbers from 2 through 6. (Note that 2 and 6 themselves do not work, since these are "strict" inequalities, not "greater than or equal to.")

Sarah's approach is correct, but she got the wrong answer. The second part of her analysis should be:

-(x-4)>2
*-1 = *-1 multiply by -1
x-4<-2
+4 = +4 add 4
x<2 plot this also

Answer 3

|x-4|>2
This simply says that -2 > x-4 > 2, or
2>x>6

On a number line put a circle at +6 and then an arrow from there going to the right forever.

Then put a second circle at +2 and draw an arrow going from there to the left forever.

Another way to look at it is x is all real numbers except where 2 =< x =< 6

Answer 4

sometimes absolute value problems can be tricky.

|x-4| > 2

x-4 > 2
x > 6

we also want the case with the value inside absolute value brackets is less than -2 because the absulte value of anything less than -2 will be greater than 2.

x-4 < -2
x < 2

so either x> 6 or x < 2