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How do you graph the inequality #4x-2y<-3#?

Answer 1

Kennedy Adams

See below

#4x-2y<-3#

Subtract #4x# to both sides

#-2y<-4x-3#

Divide through by #-2# and change the direction of the inequality.

#y>2x+3/2#

Now consider the limiting case where: #y=2x+3/2#

This is the straight line with slope #2# and #y-#intercept of #+3/2#

Then the graphic representation of the inequality is the area of all points where #y# is greater than but not equal to values on this line. Shown as the shaded area below.

graph{4x-2y<-3 [-12.66, 12.65, -6.33, 6.33]}

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Answer 2

Eli Assouline

To graph the inequality (4x - 2y < -3), follow these steps:

Rewrite the inequality in slope-intercept form, solving for (y): [4x - 2y < -3] [2y > 4x + 3] [y > 2x + \frac{3}{2}]
Plot the boundary line (y = 2x + \frac{3}{2}). This line is dashed because the inequality is strict (not including the boundary).
Since the inequality is (y > 2x + \frac{3}{2}), shade the region above the boundary line. This indicates all the points where (y) is greater than (2x + \frac{3}{2}).

That's how you graph the inequality (4x - 2y < -3).

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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.

How do you graph the inequality #4x-2y&lt;-3#?

How do you graph the inequality #4x-2y<-3#?