Question

|3x-2| = |2x - 11|
do i set these to zero? how does this work exactly?

Answer 1

remember that |x| = k can be solved by
x = k and x = -k ?

Answer 2

this is true when k is positive and negative respectively

Answer 3

so if x>2/3, 3x-2 = |2x-11|

Answer 4

if x<= 2/3, 2-3x = |2x-11|

Answer 5

you just do the same thing with the resulting two equations.

you will have a total of four eqn. you will have to solve

Answer 6

The only thing you have to be very careful is the fact that you are
using absolute values in an equation.
This makes the problem very likely to have an extraneous solution,
so you need to check your answers once you get them.

Answer 7

thank you very much yuki

Answer 8

just to let you know, solving this by graphing would make it a lot easier

Answer 9

so if you are interested, try graphing on a calculator as

y = |3x-2|
y = |2x-11|

you will see two "V-shaped lines"
the intersections will give you the answer