SOLUTION: solve for y: 2x + 4y

SOLUTION: solve for y: 2x + 4y > 2y + 6x

Question 71230: solve for y: 2x + 4y > 2y + 6x
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
2x + 4y > 2y + 6x
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Treat this just as you would an equation ... the only difference being that if you have to multiply or divide both sides by a negative number, you reverse the direction of the inequality sign.
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Let's begin by eliminating the 2y on the right side. Do this by subtracting 2y from both sides. When you do that, the inequality becomes:
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2x + 2y > +6.
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Now let's get rid of the 2x term on the left side by subtracting 2x from both sides. After the subtraction the equation is:
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2y > -2x + 6
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Finally, to solve the inequality for y, divide both sides by 2. When you do, the equation becomes:
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y > -x + 3
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Now just suppose the inequality sign is an equal sign. What would we have? The answer is the equation of a line that has a graph having a slope of minus 1 and an intersection with the y-axis at +3. Plot that graph.
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The inequality equation tells us that the values of y have to be greater than -x + 3. Therefore, you can shade in the area ABOVE the graph. That is the solution. Y can lie anywhere in the shaded region. Note that y cannot be ON the line because for that to be true y must EQUAL -x + 3. We found that y must be greater than -x + 3, so it must be above that line.
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Hope this example helps you see how to manipulate inequality equations. Note that we did not have to multiply or divide by a minus number to solve for +y, so we did not have to reverse the direction of the inequality.
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