a. -3≤ 3-5x/3 <3/8
b. 3x-5/x >0

When typing algebra, you must put parentheses around 
numerators and denominators if they contain more than 
1 letter or 1 number, like this

a. -3≤ (3-5x)/3 <3/8
b. (3x-5)/x >0

----------------------------

 

Multiply thru all 3 sides by 24





Add -24 to all 3 sides:





Divide through by -40 which reverses
the inequalities





-------------------------------

b. (3x-5)/x >0

Critical values are when numerator equas zero and when
denominator equals zero.

Numerator=0
3x-5 = 0
  3x = 5
   x =  =    <-- critical value

Denominator = 0
   x = 0

Put critical values on number line:

------------o------o---------------
            0     

Test any value less than 0, say -1, by substituting
in the original:











That's true so we shade line left of 0

<===========o------o---------------
            0      

---------------

Next test any value between 0 and , say 1, by substituting
in the original:










That's false so we do not shade line between 0 and . We
still have

<===========o------o---------------
            0      

-----------------

Test any value right of , say 2, by substituting
in the original:











That's true so we shade line right of 

S

<===========o------o==========>
            0      

Interval notation 



Edwin