Help me solve |2-3x|<=4

Just stuck on this one for some reason :/

You have two problems: 2-3x<=4 and 2-3x>=-4

2-3x<=4
-3x<=4-2
-3x<=2
x<=2/-3
x>=-2/3

2-3x>=-4
-3x>=-4-2
-3x>=-6
x>=-6/-3
x<=2

-2/3 <= x <= 2

First re write as |3x – 2| ≤ 4 Now divide through by 3 and get:

| x – 2/3 | ≤ 4/3. This describes an interval with center 2/3 and distance from the center of 4/3, like so:


......... –4/3 ......... +4/3
──●───────┬──────●──►x
.. –2/3 .......... 2/3 ........... 6/3=2

So just add and subtract 4/3 from the center to get the endpoints. The ≤ relation says the solution is in between the two end points, so reading from the diagram ...

–2/3 ≤ x ≤ 2

With this geometric approach using the form | x – a | = b being two points with center a and end points a – b and a + b, you can do these instantly, including the = case, < (inside) or > (outside) in a few seconds.

2-3x=/<4
-2 -2
-3x=/<2
divided by -3
-.66666667

CHECKING
2-3(-.666666667)=/<4
2-(-2)=/<4

Separate into 2 equations
2-3x=4 and 2-3x=(-4)
Subtract 2 from both sides and get -3x= 2 and (-6)
Divide both sides by -3 and ur answer is x=(-2/3) and 2

-(2/3) <= x <= 2