How do you graph the inequality #2x + 3y > 6#?

Answer 1
First draw a lightly dashed version of the line #2x+3y=6#, which is equivalent to #y=-\frac{2}{3}x+2# (a line with a slope of #-2/3# and a #y#-intercept of #y=2#...also note that the #x#-intercept is #x=3#).
Next, note that the point #(0,0)# does not satisfy the inequality #2x+3y>6#. Therefore, shade in the "half-plane" on the other side of the line #2x+3y=6# from the side that #(0,0)# is on. Make sure the line #2x+3y=6# remains lightly dashed. It's not part of the solution set.
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Answer 2

To graph the inequality (2x + 3y > 6), follow these steps:

  1. Start by graphing the line (2x + 3y = 6) as if it were an equation. To do this, rearrange it into slope-intercept form: [ 3y = -2x + 6 ] [ y = -\frac{2}{3}x + 2 ]

  2. Plot the y-intercept at (0, 2) and use the slope of ( -\frac{2}{3} ) to find another point. For example, move 3 units to the right (because the denominator of the slope is 3) and 2 units down from (0, 2) to get another point at (3, 0).

  3. Draw a dashed line through these two points. The line represents the boundary of the inequality, but since the inequality is strict ((>) not (\geq)), we use a dashed line.

  4. Choose a point not on the line to determine which side of the line is the solution region. A common choice is the origin (0, 0). Substitute the coordinates into the original inequality: [ 2(0) + 3(0) > 6 ] [ 0 > 6 ]

  5. Since 0 is not greater than 6, the region containing the origin (0, 0) is not part of the solution. Therefore, shade the region that does not contain the origin. This shaded region represents the solution to the inequality (2x + 3y > 6).

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Answer from HIX Tutor

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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