How do you solve and graph #2x - 3y > 6# and #5x + 4y < 12#?
Solve and graph system of linear inequalities in 2 variables:
2x - 3y > 6
5x + 4y < 12
Bring the inequalities to standard form: (1) 2x - 3y - 6 > 0 (2) 5x + 4y - 12 < 0 First, graph Line (1): 2x - 3y - 6 = 0 by its 2 intercepts. make x = 0 --> y = -3. Make y = 0 --> x = 3. To find the solution set of inequality (1), use the origin O as test point. Replace x = 0 and y = 0 into (1). We get -6 > 0> Not true. Then, the solution is the area that doesn't contain O. Color or shade it. Next, graph the Line (2): 5x + 4y < 12 by its 2 intercepts. Use O as test point. We get -12 < 0. True. Then, the solution set is the area containing O. Color it. The compound solution set is the commonly shared area. graph{2x - 3y - 6 = 0 [-10, 10, -5, 5]} graph{5x + 4y - 12 = 0 [-10, 10, -5, 5]}
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To solve the system of inequalities (2x - 3y > 6) and (5x + 4y < 12), you first solve each inequality separately for (y):
For (2x - 3y > 6): [2x - 3y > 6] [-3y > -2x + 6] [y < \frac{2}{3}x - 2]
For (5x + 4y < 12): [5x + 4y < 12] [4y < -5x + 12] [y < -\frac{5}{4}x + 3]
Now, you graph each inequality on the same coordinate plane. The solution to the system will be the region where both shaded areas overlap.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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