Write an absolute value inequality whose solution set is given by the interval notation:?

Question

(-∞, -5] U [5,∞)

AND:

For another problem with an absolute value equation I got quickmath.com to solve it for me, but I have to choose between two good answers: {7,3/5} or {7,-3/5}. The problem was; |3y+2|=|2y-5|

Answer 1

l x l > or = to 5.

This becomes x >= 5 for x>0
-x >= 5 for x<0 or x<=-5
This gives exactly your interval

l 3y+2l = 3y+2 if 3y+2 >=0 y>=-2/3

l 3y+2l = -3y -2 if 3y+2<0 so y<-2/3

l2y-5l = 2y-5 if 2y-5>=0 so y>=5/2

l2y-5l =5-2y if 2y-5 <0 so y<5/2

So you have the following values -2/3 ..... 5/2

Case1: y<-2/3 we get: -3y-2 = 5-2y so -y= 7
or y=-7 which is a solution because it is <-2/3.
Case2: y>-2/3 but y<5/2 we get 3y+2 = 5-2y
or y= 3/5 which is a solution because it is inside interval
Case3: y>5/2 we get 3y+2=2y-5 so y=-7 which is not inside the interval.

So the only solutions are: y=-7 and y=3/5.

THESE ARE SOLUTIONS NOT AN INTERVAL. TO HAVE AN INTERVAL YOU NEED AN INEQUALITY NOT AN EQUALITY.

Answer 2

Well, you know that with the first one, if you write in normally it says...

x <= -5 or x >= 5

So, now to write the equation.... I have no idea, sorry.

For the second...

|3y + 2| = |2y - 5|

3y + 2 = 2y - 5
y = -7

-3y - 2 = -2y + 5
-7 = y

Hm.. I just kep the -7. Okay, I tried. I give up.

Answer 3

you keep in mind that substituting x for -a million or for 6 will yield a nil equality. yet this equation is an inequality and means that any fee that yields a adverse answer (on the left fringe of the equation) satisfies the circumstances of the equation. So, what if x equals 0? (0 + a million)(0 - 6) = a million(-6) = -6 enable's keep on with the numbers between our 2 techniques (-a million and six). So try a huge determination like 5. (5 + a million)(5 - 6) = 6(-a million) = -6 in certainty, any huge variety between -a million and six will yield a adverse result. yet we already comprehend that -a million and six yield a nil, which isn't < 0. So in notation period: Your answer sounds like this: (-a million,6). The parenthesis ability the period between -a million and six except both numbers. ok! it truly is definitely below 0.

Answer 4

|x| >= 5

for a graph, go to www.quickmath.com, click Plot under Inequalities, then type that in exactly as i have it and then click plot.

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|3y + 2| = |2y - 5|

3y + 2 = 2y - 5
y = -7

3y + 2 = -(2y - 5)
3y + 2 = -2y + 5
5y = 3
y = (3/5)

ANS : y = -7 or (3/5)

Now matter how you change the problem around, you will still get y = -7 or (3/5)

Answer 5

|x| ≥ 5

Answer 6

(-∞, -5] U [5,∞) corresponds to | x | >= 5

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|3y+2|=|2y-5|

that is, 3y+2= 2y-5 or 3y+2= - ( 2y-5 )

that is, 3y -2y = -5 -2 or 3y+2y = +5 -2

that is, y = -7 or 5y = 3

that is, y = -7 or y = 3/5

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remember that

|x| < k corresponds to -k < x < k or the open interval (-k,k)

|x| > k is the complement of |x| < k

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also |x| = k implies x= k or x= (-k)