Here is the solution for the problem below. I was impressed at your thinking and methods in attempting to solve the problem. Beautiful job!!!! My only concern is very few or you proceeded to tell me what the "?" numbers were. Than means that many of you didn't address the actual question asked. Please read carefully. ;-)
Suppose that we are told that four numbers a, b, c, d lie between −5 and 5. Suppose also that the numbers are constrained so that
5 is less than a+b which is less than 10 and −10 is less than c+d which is less than −5
Given this information, what can you conclude about these inequalities?
A.M.
ReplyDeleteGiven these inequalities, I conclude that A+B can only be an answer between 6-9. It is greater than five and less than ten, which told me that it had to be 6, 7, 8, or 9. I can also conclude that C+D is greater than -10 and less than -5. This gives me the information that C+D could be between -6 and -9. This also allows me to conclude that A+B is most likely going to be great than C+D.
J.H
ReplyDeleteWhat we could conclude about the data is that if 5 less than a+b which is less than 10 and -10 are less than c+d and that is less than -5. The equation could look like, 5<a+b<10 and the other equation could be -10<c+d<-5. With the inequalities you could say that the first output of the equation would be smaller than the second output.
C.A.
ReplyDeleteWhat you can conclude about these inequalities is that if you know that 5 is less than a+b which is less than 10 and −10 is less than c+d which is less than −5, then you can make that easier to write. The inequalities would look like this: 5<a+b<10 and -10<c+d<-5. You can conclude that the values of the inequalities to the left are all less than the ones to the right in each inequality.
A.A.M.
ReplyDeleteWhat you can conclude about this data is that if 5 is less than a+b which is less than 10 while -10 is less than c+d which is less than -5. So what the equation could look like is 5<a+b<10 and the other equation could be -10<c+d<-5. With the given inequalities you could conclude that the first output of the inequalities is smaller than the second output. You can also conclude that you need to use smaller numbers for the first output and then you have to use larger numbers for the second output.
MNH
ReplyDeleteA= 5
B= 1
C= -5
D= -1
1.) 5<5+1-(-5)-(-1) <12=5<10<12
2.) 5<5-(-5)<12=5<10<12
3.) 5<5-(-5)+1-(-1)<15=5<12<15
4.) 20<5(1)(-5)(-1)<30=20<25<30
___
5.) -5<5+5-V 5(5)<10=-5<0<10
2
S.R.
ReplyDeleteA=5
B=1
C=-5
D=-1
1. 5<5+1-(-5)-(-1)<12= 5<10<12
2. 5<5-(-5)<12= 5<10<12
3. 5<5-(-5)+1-(-1)<15= 5<12<15
4. 20<5(1)(-5)(-1)<30=20<25<30
5. -5<5+5-V 5(5)<10=-5<0<10
2
MJH
ReplyDeleteA=5
B=4
C=-4
D=-3
1. 15, 17
2. 8, 10
3. 1, 3
4. 239, 241
5. 0.02, 0.04
E.D.
ReplyDeleteI have concluded that A B C and D have the following values-
A= 3
B= 3
C= -3
D= -3
And my conclusions about them and the equtions given are:
<a + b – c – d<
<3 + 3 - -3 - -3<
<3 + 3 + 3 + 3<
< 6 + 6 <
< 12 <
13<12<11
<a – c<
<3 - -3<
<3 + 3<
< 6 <
7< 6 <5
<a – c + d – b<
<3 - -3 + -3 – 3<
< 3 + 3 + -3 – 3<
< 6 + -6<
<0<
1<0<-1
<abcd<
<3 3 -3 -3<
<9 -9<
<-81<
-80<-81<-82
<|a| + |c| - square root of ac<
_______
2
<3 – 3<
<0<
1<0<-1
A.B.
ReplyDeleteBased off the given information, I can conclude that there is more than one possible answer for what the variables are and for what the question marks are, but they are very specific. I think that variables a and c need to be opposites (they have equal amount of values away from zero), as well as variables b and d.
Ex. {1, 2, -1, -2} {2, 3, -2, -3} {4, 5, -4, -5}
This is because if they are opposites, the last inequality will be greater that -1 and less than 1, which will always be zero in this case.
The four numbers that I chose were {3, 4, -3, -4}. Based off of my numbers, these are the answers for the inequalities (n being my final answer).
1. 13 is less that n which is less than 15
2. -2 is less than n which is less than 0
3. 13 is less than n which is less than 15
4. -1 is less than n which is less than 1
Overall, I think that the last inequality shows the most about what the variables are. The variables will always have the same absolute value.
N.H
ReplyDeletea= 5
b= 1
c= -4
d= -3
1. 10, 14
2. 7, 10
3. 4, 6
4. 59, 61
5. -1, 1
S.G.
ReplyDeleteSuppose that we are told that four numbers a, b, c, d lie between −5 and 5. Suppose also that the numbers are constrained so that
5 is less than a+b which is less than 10 and −10 is less than c+d which is less than −5
given this information, what can you conclude about these inequalities?
-5(a,b,c,d)5
5 is less than a+b which is less than 10.
-10 is less than c+d which is less than -5.
What I can conclude about these inequalities is that a must be 4, and b must be 4. Because if a equals 4, and b equals 4, then a+b equals 8, which means 5 is less than the sum of a+b. Also, it’s less than 10, so it is inside of its “boundaries”. I also think that c equals -4, and d equals -4. Because if c and d equal -4, then c+d equals -8, which means -10 is less than -8. Also, it’s less than -5. So it also stays within it’s boundaries. So the answers are,
A= 4
B= 4
C= -4
D= -4
M.O.
ReplyDelete5<a+b<10
-10<c+d<-5
__<4+-2-(-4)-2<__
__<4+-2+4-2<__
__<2+4-2<__
__<6-2<__
__<4<__
__<4-(-4)<__
__<4+4<__
__<8<__
__<4-(-4)+2-(-2)<__
__<4+4+2+2<__
__<8+2+2<__
__<10+2<__
__<12<__
__<4*-2*-4*2<__
__<-8*-4*2<__
__<32*2<__
__<64<__
A=4
B=-2
C=-4
D=2
Given the inequalities, I have concluded that using opposites as A, B, C, and D creates a legitimate equation. It also creates a range of numbers that never, in fact, make it into the negatives. The range I would give for these inequalities is 0-64 or 64.
I used opposites to substitute for my variables because it seemed like a good theory to go on, according to one of my friends. Using 4, -2, -4, and 2 does not change any answers by changing around the numbers. I changed most of my negative numbers to positive numbers when there was a subtraction symbol.
On the last inequality, which is kind of hard to write on the computer, was 4 plus 4 divided by 2 minus the square root of 16. So then it became 8 divided by 2 minus 4 then 4 minus 4 and the final product is zero.
P.M.
ReplyDeleteI conclude that for all the inequalities these are numbers that work for all of them. These numbers follow the requirements, and through process of elimination, I have figured out that these numbers work. I have tested them for each equation.
A = 5
B = 1
C = -4
D = -3
So…
1. 10, 14
2. 7, 10
3. 4, 6
4. 59, 61
5. -1, 1
JBR
ReplyDeleteGiven the information I can conclude that basically the numbers are just inequalities either negative and/or positive. For a and b they were in between 10-5. For c and d they were between -5 and -10.
A+B-C-D
A= 5 B= 4 C= -4 D= -3
1. 15,17
2. 8, 10
3. 1, 3
4. 239, 241
5. 0.02, .04
N.H
ReplyDeletea= 5
b= 1
c= -4
d= -3
1. 10, 14
2. 7, 10
3. 4, 6
4. 59, 61
5. -1, 1
I got my answer by trying to have a solution to the information at the beginning. After doing this, I plugged the numbers in, and tried to solve the problems. They seemed to work, so this was my answer. This worked because I double-checked my answer to ensure that they were correct.
M.W.
ReplyDeleteGiven the inequalities, I can conclude that there is a range of numbers that may be used for substituting the variables, a,b,c and d. By using opposites, I can figure out that in order to make an accurate equation, variables a and c have to be opposites and b and d have to be opposites. For example, the numbers I got for the variables are, a is 2, and c is -2, and b is 4, and d is -4.
I figured this out by using the given inequalities. The last inequality shows that you have to use opposites by using absolute values. If I plug in a, b, c, and d, into the last inequality given the numbers I found, the answer would be 2-2=0. This shows that the numbers for a,b,c, and d have to be opposites.
A=2
B=4
C=-2
D=-4
M.N
ReplyDeleteSuppose that we are told that four numbers a, b, c, d lie between −5 and 5. Suppose also that the numbers are constrained so that
5 is less than a+b which is less than 10 and −10 is less than c+d which is less than −5
given this information, what can you conclude about these inequalities?
a+b is more than 5. a+b is less than 10. -10 is less than c+d which is greater than -5
1. 5<4+3-6-3<-5
2. 8<
The first thing I did was to rewrite the requirements because they didn’t make sense to me at first. Then I made sure that c+d had all the numbers in between -5 and -10. Then I made sure that a+b had all of its numbers in between 5 and 10.
MD
ReplyDeleteSuppose that we are told that four numbers a, b, c, d lie between −5 and 5. Suppose also that the numbers are constrained so that
5 is less than a+b which is less than 10 and −10 is less than c+d which is less than −5
Given this information, what can you conclude about these inequalities?
Given this information, we can conclude many things about the inequalities. First I knew that a+b is greater than 5. But also b is less than ten. So I knew that a plus less than ten is greater than 5. I also knew that the numbers lie between 5 and -5. That means that a plus (5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5) is greater than 5.
But then I realized that what the problem was really saying was that a+b is less than ten and greater than five. Since the numbers lie between 5 and -5, we know a few things. The answer to a+b must be 6, 7, 8, or 9. A and b can’t be negatives, because that would mean that to get it greater than 5 the value of the other number would have to be 6 at the least. But I did know that the first question marks must equal ten, because 9,8,7, and 6 are less than ten.
Then I moved on to c and d. I knew that c-d was greater than -10 and less than -5. But also the numbers lie between 5 and-5. So I had to figure out what minus what was greater than -10 but less than -5 while still staying in the region of 5 and -5. So we know that c-d must be -9, -8, -7, or -6.
I was starting to get really impatient and confused because the problem was almost impossible. The problem was that everyone else was trying to solve for the variables. However, the question does not ask for the value of the variables, it asks for what we can conclude about the inequalities. Plus, there aren’t any equal signs in the inequalities, so it’s not an equation, so the values of a,b,c, and d could have many different values and we can’t figure out exactly what they are because all we know, for example, is that a+b is less than ten and greater than 5, it does not say exactly what the answer for a+b is, it just gives you options.
S.A
ReplyDeleteJ.S
4 numbers between -5 and that the numbers are constrained so that
5 is less than a+b which is less than 10 and −10 is less than c+d which is less than −5
Given this information, what can you conclude about these inequalities?
A plus b = 6 through 10
C plus d = -6 through -10
a and b and c and d are between -5 and 5
a could be 1 through 5
b could be 1 through 5
c could be -1 through -5
d could be -1 through -5
5 <a +b < 10
-10 <c +d <-5
1. 11.99<a +b-c-d<18.01
2. 1.99<a-c<10.01
3. 1.99<a-c +d-b<8.01
4. 24.99<abcd<400.01
5. about -0.40 < (lal + lcl) / 2 – vlacl<0.01
How we solved for the lowest number you can get was that we plugged in the lowest number for a and b that still followed the constrains and then plugged in the highest numbers for c and d that still followed the constrains. Then for the highest number you can get we plugged in the highest number for a and b then the lowest numbers for c and d that still follow the constrains. I can conclude that there is a range of numbers that a b c and d can be
B.H.
ReplyDeletea+b is more than 5. a+b is less than 10. c+d is more than -10. c+d is less than -5.
10>a+b>5 -10<c+d<-5
a+b=6, 7, 8, 9 c+d=-6,-7,-8,-9
1. 5<a+b-(c)-(d)<-5
2. <a-(c)<
3. <a-(c)+d-(b)<
4. <abcd<
5. <a+c sqr. rt. of abs. val.(ac)
2
What I can conclude about the inequalities is that you can not answer all of the problems with the same answers.
JS
ReplyDeleteOctober 8 POW
• To help us find a solution from the problem we found a way to re-write the problem. We came up with a+b is greater than five, but b is less than ten. The equation for the fist part (a+b) would be a+>10= <5. Now we just have to find a way to solve. B can be (5,4,3,2,1,0,-1,-2,-3,-4,-5) because it has to be less than ten. We concluded that the whole expression is less than 5, so the solution can only be from 4 through -5. I am guessing that since we don’t know much about a, the solution may be harder to find especially for that variable.
• After being helped by a fellow student, we realized that we were probably over thinking the inequality. After being helped, we have a new conclusion that says that a+b is less than ten, but greater than five. So what we really need to find is the sum of two numbers that equal 6, 7, 8 or 9. After plugging in 5+4=9
• After re-evaluating again, we concluded that those numbers only worked for the first example, and our classmate was not accurate. We thought about it and what the classmate did help us on was that we know the sun of a+b is indeed 6, 7, 8 or 9.
• We got confused when we approached the other half of the inequality (c-d). The boundaries of the numbers in the whole problem are in-between -5 and 5. But, we concluded that the sum of c-d is greater than -10 and less than -5. So we need to find two numbers that are in-between -5 and 5 that equal an answer of -9, -8, -7, and -6.
• We didn’t find the numbers, but if we had more time to follow through with our steps, we could probably get the answers because after working together I have a better understanding of the problem and the variables. I think that even if you don’t get the exact numbers that the mind-process is just as important and what we concluded seemed reasonable and accurate.
O.S
ReplyDelete5 is less than a+b
a+b is less than 10
That means that a and b could be anything between 6 through 9.
-10 is less than c+d
c+d is less than -5
That means that c and d could be anything between -6 through -9
So, for <a+b-c-d<, it would go like this: (6,7,8,9)+(6,7,8,9)-(-6,-7,-8,-9)-(-6,-7,-8,-9)
Then, if <a-c<, then it goes like this: (6,7,8,9)-(-6,-7,-8,-9)
And: <a-c+d-b<, so (6,7,8,9)- (-6,-7,-8,-9)+ (-6,-7,-8,-9)- (6,7,8,9)
And for <abcd< : (6,7,8,9) (6,7,8,9) (-6,-7,-8,-9) (-6,-7,-8,-9)
Finally, <|(6,7,8,9) |+ |(-6,-7,-8,-9)|
--------------------------------- - √|(6,7,8,9) (-6,-7,-8,-9)
JL
ReplyDeleteSuppose that we are told that four numbers a, b, c, d lie between −5 and 5. Suppose also that the numbers are constrained so that
5 is less than a+b which is less than 10 and −10 is less than c+d which is less than −5
Given this information, what can you conclude about these inequalities?
10<5+4-(-4)-(-3)<20
??<a+b-c-d<??
0<5-(-4)<10
??<a-c<??
-10<5-(-4)+(-3)-4<10
??<a-c+d-b<??
??<abcd<??
??<a+c/2-ac<??
Given the information, we can conclude many things about the inequalities. The first thing I figured out was that the sum of a+b must be less than 10 and greater than 5. I also know that the numbers must lie between -5 – 5(-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5). Then I moved on to c+d. I figured out that the sum must be more than -10 and less than -5.
A=5
B=4
C=-4
D=-3
JL
ReplyDeleteSuppose that we are told that four numbers a, b, c, d lie between −5 and 5. Suppose also that the numbers are constrained so that
5 is less than a+b which is less than 10 and −10 is less than c+d which is less than −5
Given this information, what can you conclude about these inequalities?
10<5+4-(-4)-(-3)<20
??<a+b-c-d<??
0<5-(-4)<10
??<a-c<??
-10<5-(-4)+(-3)-4<10
??<a-c+d-b<??
??<abcd<??
??<a+c/2-ac<??
Given the information, we can conclude many things about the inequalities. The first thing I figured out was that the sum of a+b must be less than 10 and greater than 5. I also know that the numbers must lie between -5 – 5(-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5). Then I moved on to c+d. I figured out that the sum must be more than -10 and less than -5.
A=5
B=4
C=-4
D=-3