2|x-10|<3 express as an interval?

Answer 1

divide by 2 on both sides => | x-10|< 3/2

now either x -10 < 3/2 or -(x-10) < 3/2

if x-10 < 3/2 then x< 3/2 +10
in this case x <11.5

if -x+10 <3/2 then x > 10 - 3/2
in this case x > 8.5

so we see that 8.5 < x <11.5

what is this in interval notation (8.5,11.5)

The last thing we should do is check our answer so lets pick a couple numbers to see if everything worked, (you don't need to do this but it always helps if you check your work)

here are two that should work:
9 for instance 2|9-10| = 2|-1| = 2 < 3 so 9 checks out

11 : 2|11-10| = 2|1| =2 < 3 so 11 checks out

Answer 2

6-10

Answer 3

2|x - 10| < 3

|x - 10| < 3/2

-3/2 < x < 3/2

17/2 < x < 23/2

x is an element of [17/2, 23/2]

Answer 4

|x-10| < 3/2
x - 10 < 3/2 and x - 10> -3/2

x < 11 1/2 and x > 8 1/2

8 1/2 < x < 11 1/2

Answer 5

divide both sides by two, giving you

|x-10| < 1.5

because it is an absolute value we have to set up an two inequalities.

so x-10 < 1.5
and -x +10 < 1.5

soliving gives us x > 8.5 and x < 11.5, which in interval notation, looks like: (8.5, 11.5)