Question

Solve : |2 – x| < 3

Answer 1

\[|a| < b \iff -b < a < b\]

Answer 2

If you have one, you can rewrite it as the other.

Answer 3

So in this case you can re-write your problem as

\[-3 < 2-x < 3\]

Then you just solve simultaneously for the bounds of x.

Answer 4

Of course, don't try and use the opposite sign in the same rule...because it's not true that
|a| > b => -b > a > b.

For that you need to use an "or"

a < -b OR a > b

Answer 5

-1,5?

Answer 6

or -5,1?

Answer 7

-1,5 <----awnser

Answer 8

Keeping with polpak's response,

-3 < 2 - x < 3
-5 < -x < 1
5 > x > -1

So, x is between -1 and 5.

Answer 9

Remember you have to switch the direction of the inequality when multiplying or dividing by a negative number.