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

i need to solve the inequality 6x-4y<12

### 3 Answers by Expert Tutors

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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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.

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

Thank you Michael.
Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (6 lesson ratings) (6)
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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

Christine K. | Experienced TutorExperienced Tutor
4.9 4.9 (92 lesson ratings) (92)
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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