|
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
.
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.
.
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:
.
2x + 2y > +6.
.
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:
.
2y > -2x + 6
.
Finally, to solve the inequality for y, divide both sides by 2. When you do, the equation becomes:
.
y > -x + 3
.
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.
.
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.
.
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.
|
|
|
| |
