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

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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.

-4y < 12 - 6x

-4 -4 -4

When you divide by a negative number, you should flip the inequality sign. 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 < 3 x - 3

2

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

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.

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

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