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how do i solve the inequality 6x-4y<12

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3 Answers

 This you can have the graphical solution:
 
 Graph the line :
 
    6X - 4y = 12
 
   by   X intercept  2 and Y intercept of -3
 
   Then test  a point to the right , i.e.   ( 0,0 )
 
       6( 0) - 4 ( 0 ) < 12
   
      Then shade all area to the right of the line as solution. Dash  the line too, because points on the line are not the solution.

Comments

The x-intercept is the point where y=0, that is at x=2
The y-intercept is the point where x=0, that is at y=-3
 
6x-4y<12 add 4y to both sides
6x<4y+12 subtract 12 from both sides
6x-12<4y divide by 4
(6/4)x-3<y or rewrite in more conventional form
y>(3/2)x-3
The solution is all of the points in the plane strictly above the line y=(3/2)x-3
 
You should solve an inequality just like you would solve an equation, except copy your inequality signs instead of the equals (=) sign.  So you want to solve this for y.
 
First, you should isolate the -4y by subtracting 6x from both sides of the inequality.
  6x - 4y < 12
 -6x               -6x
      -4y < 12 - 6x
 
Next, you would divide both sides by -4 to get y by itself.
  -4y126x
 -4      -4    -4
 
Then simplify and write your answer in standard form which would be with the x-term in front of the numerical term.
y < -3 + 3x
            2
y < x - 3
      2

Comments

Would you please revise.  When an inequality is divided or multiplied by a negative number, the inequality flips.
-4y<12x-6 divided by -4 becomes y>-3x+6/4.