Which of the following ordered pairs is a solution to the inequality?

Question

accidentalaichan · Answer

$$y \ge 4x - 2$$

accidentalaichan · Answer

A. (0, −4) 

B. (0, 0) 

C. (0, −3) 

D. (0, −5)

e.mccormick · Answer

Well, do you know how to find the area that is the solution to an inequality?

e.mccormick · Answer

You can do it that way, or you can just try them out and see which works.

accidentalaichan · Answer

okay, so I did my inverse operations, adding 2 to each side
$$2y \ge 4x$$
But now I'm lost

e.mccormick · Answer

How did you get 2y?

accidentalaichan · Answer

I added 2 to each side. It wasn't right, was it?

e.mccormick · Answer

That would be 2+y, not 2y, but there is no need.  $y\ge 4x-2$ is in slope-intercept form, so there is no real need to do anything else to the equation.  You can graph it pretty quick, or just try points.

 $y\ge 4x-2$ for  (0, −4) 

 $(-4)\ge 4(0)-2$

 $-4\ge 0-2$

 $-4\ge -2$

Because -4 is less than -2, that is false and not an answer.

accidentalaichan · Answer

Oh, I see.

accidentalaichan · Answer

Thanks

e.mccormick · Answer

np.  I'll also show the graphing method.

e.mccormick · Answer

To graph it, easy way is to find the intercepts: (0,?) and (?,0).  Just use = for that.
$0= 4x-2$
$2 = 4x$
$2/4 = x$
$1/2 = x$

So (1/2,0) is the x intercept 

$y= 4(0)-2$
$y= -2$

And (0,-2) is the y.

I can draw a line through those two points.  Because the question uses $\ge$ it is a solid line.
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