Parviz F. answered • 11/15/13

Mathematics professor at Community Colleges

Parviz F.

11/16/13

Katy H.

asked • 11/12/13i need to solve the inequality 6x-4y<12

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Parviz F. answered • 11/15/13

Tutor

4.8
(4)
Mathematics professor at Community Colleges

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.

Parviz F.

Thank you Michael.

Report

11/16/13

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.

-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

Michael F.

tutor

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.

Report

11/16/13

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Michael F.

11/15/13