For each of the equations below:
1. Solve each equation for the variable.
2. Explain each step you took to solve the problem and find the value of the variable.
3. Justify your reasoning for using the steps that you did to solve the equation.
Equation A: 7t = 10t + 18
Equation B: 14u – 7 = -14 – 7u
4. Compare the two equations. What was the same about them? What was different about them? What did you have to do differently for each of the problems to find the value of the variable?
A gentle reminder:
Assignment - In your comment remember to include the following:
* your name (first name and last initial)
* your class
* the answer to the problem – there are THREE parts for each equation and then ONE final question about both – be sure to include every part and number the parts
* an explanation that includes the strategy you used to solve.
* is there another way to solve the problem?
* any additional thoughts you have about the problem(s)
*** Please be sure to comment on Blog Assignment #5 so that your assignment is not lost on other posts! ***
Remember when you "publish the comment" it will not appear on the Blog until it is past the due date AND Mrs. DaSilva has a chance to read and approve it.
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A.7t=10t+18
ReplyDeleteAnswer:T=1 1/2
b.14u-7=14-7u
Answer:U=2
Dylan.D
Class:1
1.+2.)
ReplyDelete1u=10t+18
-7t\-7t
3t=18
/3(\)/3
1t=6
14u-7=-14 - 7u
-7u\7u
7u-7=14
-7\-7
7u=7
/7(\)/7
1u=1
3.
I used the factoring method to do this problem because its is an easier way to fingd the answer when you are useing variables.
4.They are both the same because they are cboth equatinos.they are both different because they both have different answers. acctualy I used the same maethod to find both of them I used factoring method.
Math 4 MoNsTeR A.K.A Garrett
joseph alden math 4
ReplyDelete7t=10t+18
-7t -7t
3t+18
-------------------------------------------------
14u-7=-14-7u
-7u -7u
7u-7=-14
7u-(-21)
7u+21
Gian.M
ReplyDeleteClass.4
Problem A:I subtracted 7t from each side and on the left side i got zero and on the right i got 3t+18. Next i divided 3 by 18 and that mean that t=6
Problem B:I added 14u+7 for the left side and that equaled 21u and for the right side i got 7u+14 and got 21u and if you divide that by 21u you get u=1.
My strategy was to do the problem out on a separate sheet of paper then explained what my work looked like back onto the blog.
This would be the easiest way to explain those equations.
Kirby Forsberg Math-4
ReplyDelete7t = 10t+18
- 7t – 7t .
0 = 3t+18
-18 -18
-18= 3t
3 3.
-6 = t
14u – 7 = -14 – 7u
-7u -7u
7u – 7 = -14
+7 +7
7u = -7
7 7
u = -1
4: The two equations above were similar because both of their answers were negative numbers. The last step for each problem was division. Also, the first step of each problem consisted of subtracting the 7 times the variable on each side. The differences between the two problems was first of all, there were different answers, both problems required different operations to break down the equation.
!!!!!!!!!!!!!!!!!!!!!!!
I created text boxes to explain what i did on each step, but i wasn't able to copy and paste them onto this comment box
J.P Hebert
ReplyDeleteclass 3
1a) 7t = 10t + 18
(-10t)(-10t)
-3t=18
(-3t/-3)(18/-3)
t=-6
1b) 14u – 7 = -14 – 7u
(+7) (+7)
14u = -7-7u
(+7u) (+7u)
21u = -7
(21u/21) (-7/21)
u = -1/3
Colby Ferreira
ReplyDeleteMath: 4
1.
A. 6/1 or 6=t this problem involved the use of negative numbers.
B.11/7= u this problem involved the use of negative numbers.
3. I solved the problems by using the do the same thing to both sides method. I could not find any other way to solve them. I would still be willing to solve problems like this if there were different numbers or if there were bigger numbers. I found solving them, both challenging and, fun to ponder about.
4. These two problems when solved the variables are both fractions. I found no other similarities other then that they involved using knowledge about negative numbers. I used pretty much the same strategy of getting rid of the negative numbers for both problems.
Kyle damasio math 2
ReplyDeleteFor equation a 7t=10t+18 i got t = -6 . The way i got this was by first taking 7t away from both sides to get 0=3t+18 then you take away 18 and get -18=3t. Next divde by 3 to get -6 = t.
For equation b 14u-7=-14- -7u i got u = -14. The first thing i did was add the 7u and got 21u+u=-14 , then i added the seven andgot 21u+u=-7 , then i divded both by 7 and got 5u=-1.Last i divded 5u and -1 by 5 and got .2.
Both the equations did not past positive one. I would not be willing to do this with bigger numbers because it would be too confuseing.
Tess C.
ReplyDeleteMath: 2
1& 2. Equation a, I got that t=6 because I first took away 7t from both sides of the equation. Then, I was left with 3t+18. Next, I divided both 3t & 18 bye 3 & was left with t=6.
For equation b, I first subtracted 7u from both sides of the equation. Then, I was left with 7u=14. Next, I divided 7u & 14 bye 7 & I was left with u=2.
3. I used these steps because it seems to be the easiest way to solve these two equations.
4. Both these equations can be solved the same way & they both have variables on each side that aren’t the same number. But, they are different in some ways, the one problem is addition & one is subtraction. Also on both equations I started with a different first step.
The strategy I used to solve this problem was what the opposite is; I like this strategy because it is easy & works well.
There are other ways to solve this problem, but I think this way is the easiest.
Lexi Winnes
ReplyDelete3class
Equation A: 7t = 8t + 18
1.) t= (-18)
2.) First, I rewrote the equation on a separate sheet of paper. Next, I subtracted the smaller variable from each side, then subtracted 18 from each side and got -18 = t.
3.) When solving the equation, its important to do the same thing to both sides, to keep the equation even . I will repeat these steps for equation B.
Equation B:14u-7= -14 – 7u
U= -1
I solved equation B by doing to same thing in equation A, I rewrote the expression on a piece of paper, and I did the same thing to both sides.
U= -1
I solved equation B by doing to same thing in equation A, I rewrote the expression on a piece of paper, and I did the same thing to both sides.
4.) When comparing these two equations, you will notice some things similar and other things different. One thing that’s similar is the value of each variable is a negative number. The difference was the operations being used (multiplication, division, etc.). I didn’t have to do anything different to sold these problems really, just use different operations.
Blog#5 Due March 19 2010
ReplyDeleteRachael.P
math.4
Part.1)
EquationA:7t=10t+18=6t
EquationB:14u-7=-14-7u=-7u
Part.2)For equationA:7t=10t+18 i first to a sheet of paper. Then i wrote a chart like we do in math class. On the left side of the chart i put 7t and on the right side i put 10t+18. On the left side i added a 10t so it would be a little easier.I then i subtracted 3 from each side cause there a 3 t's. Then i think i crossed the tens out then go 3t over 3 a and 18 over 3 cross cancel the three on top of the first fraction and on the second the other three on the bottom 18/3=6. The next one was equationB:14u-7=-14-7u for this problem it was easier to make a chart sense there were 2 numbers on each side. When i made my chart i put 14u-7 on the left side and on the right side i put -14-7u. First thing i did was i subtracted 7 from both sides,then on the left side i got u-7 and the right side = 14. The reason why on the right i didn't get 7u even though it was the last number on that side is because usually when you do thing like this you usually have 7u-14 so that what i did, i just switched them. then i subtract 7 again on both sides. The left side is equal to zero in this case u= and the 14 minus 7 = 7,so the answer is -7.
Part3.)The reason why i used these steps to solve these two equations is that we use these steps in school in math class and this problem is like the bag problem so you can also draw scales for example equationA: you can draw 7 bags on side1 and on side2 you can draw 10 bags and 18 blocks. Sort of the same thing you can do for equationB: On side1 put 14 bags and 7 blocks and on side2 7 bags and 14 blocks the same thing as the chart but more simple for me.Thats why i did these steps there easy we are tought them and it makes sense.
Part4.)
The thing about equation a and b that were the same is they both have a variable or letter. Also are both equations and equal another equation and provide pretty much the same steps.
The things that are different are equation a has addition b is subtraction and a has t as the variable and b has a u. Also equation A is 7t=10t+18 and B make more sense cause it's a correct equation and easy cause has 2 numbers on both sides 14u-7=-14-7u. The thing that was hard about A was that it had one number on one side two on the other and it was easy but the variable was the second number usually its on the first though.
explanation... What i used was a chart and subtracted and added and used my steps and notes in class. Also i used scales to. I used this and that what i did in order to solve this problem.
Another way to solve this prtoblem is to use let statements and also use scales drawing.
thoughts... This is what i like about this problem it's easy but i think there should be another way to solve this problem. Also be a variable in 7u and there should be another number infront of it.
Equation A: 7t = 10t + 18 (7+10=17, +t=17t) +18 = 35 t. how I got this answer is because 17 + 18 = 35 + t = 35t
ReplyDeleteEquation B Equation B: 14u – 7 = -14 – 7u
14u - 7 ( 14 - 7 = 6 + u = 6u ) = -14 - 7 = -7u
How these problems were alike is because I used the same technique on the two problems.
o
Shaelyn Raposa
ReplyDeleteMath 3
1) Equation A:
7t = 10t + 18
-10t -10t
-3t = 18
-3t/3t 18/-3t
t=-6
Equation B:
14u – 7 = -14 – 7u
+7u +7u
21u - 7= -14
+7 +7
21u = -7
21u/21= -7/21
u=1/3
2)STEPS
Equation A:
To solve equation A, I first subtracted 10t from both sides to cancel out the 10t from the right side. I was left with -3t=18. Last, I divided both sides by -3 to get the t alone. I was left with my answer of t=18.
Equation B:
To solve equation B, I first added 7u to both sides. I was left with 21u - 7= -14. Next, I added 7 to both sides. I was left with 21u = -7. Last, I divided both sides by 21 to get the "u" alone. I was left with my answer if u=1/3.
3) I used these steps to solve the equation because I needed to get the variables alone. To get the variables alone I needed to do the same thing to both sides of the equation. When I did the same to both sides I would ask myself "What's the opposite?" This means I had to take a part of the equation and do the opposite to it and that would cancel it out.
4) These equations were similar because they both had a variable on both sides that you had to solve for. They were different because on equation A, you had an addition problem and on equation B, there was a subtraction problem. Also, equation B has negatives and equation B does not. I had to work with the opposites differently in the equations because equation A had addition and multiplication that I had to do the opposite to. Equation B had subtraction and multiplication that I had to do the opposite to.
STRATEGY
My strategy to solving the problem was doing the opposite to both sides to get the variable alone.
ADDITIONAL WAYS OF SOLVING
You could also solve this problem by thinking of a balance table with bags of "n" blocks and leftover blocks.
Bridget O'Hanley Math: 3
ReplyDeleteBlog#5
Equation A: 7t=10t+18
1) 7t=10t+18
-7t -7t
0=3t+18
-18 -18
-18 =3t
3 3
-6=t
2) First, I subtracted the smaller variable (7t) from both sides. (0=3t+18) Then I subtracted 18 from each side. Now I have -18=3t. Next, divide both sides by 3 to get the answer; -6=t
3) I subtracted the smaller variable from each side to get all the variables to one side. I subtracted 18 from both sides to get rid of the +18 on the right and you have to do the opposite and the opposite of +18 is -18. Then I divided both sides by 3 to get the value of one t.
Equation B: 14u-7=-14-7u
1) 14u-7=-14-7u
-7u -7u
7u-7=-14
+7 +7
7u = -7
7 7
u = -1
2) First I subtracted you from both sides which left me with (7u-7=-14) then I added 7 to each side (7u=-7). Lastly, I divided both sides by 7, leaving me with u=-1.
3) I subtracted 7u from both sides because you have to subtract the smaller variables from the bigger ones to get them all to one side of the equation. Then I added 7 to each side to get rid of the -7. After that, I divided each side by 7 to get the value of u. (-1)
4) These equations both followed the same strategy and most of the same steps. One difference between these two equations if the number. For the first one, I had to divide -18 and 3t both by 3 and I divided 7u and -7 by 7 for the second problem.
I used the strategy “do the same to both sides”. I don’t think there is another way to solve this problem. I liked this blog question because we are working on problems similar to this is class and I really enjoy solving equations like this.
math:4 mark lopes
ReplyDelete7t=10t+18
let 7t=number of block in one bag
let7t+10t equal total numbers of bags
let7t+10t+18=total number of blocks and bags
Connor Mcmullen
ReplyDeleteclass-3
1. 7t = 10t + 18
-7t -7t
0 = 3t + 18
-18 -18
-18 = 3t
/3 /3
54 = t
14u – 7 = -14 – 7u
+ 7 +7
14u = -7 - 7u
+7u +7u
21u = -7
/21 /21
u= -1/3
3. the reason i did it this way is because to solve for a variable this is the way you have to do it.
4. i had to solve each problem differently because equation A had a equation equal a answer and equation B had a equation equal an equation. the two equations were similare because you had to use the same method on both of them.
Rachel Cloutier
ReplyDeleteMath 4
Answer: For the first equation I got the answer of negative 6 equals T and for eqaution B I got postive 1 is eqaul to U.
Question 4: The things that are the same within these two eqautions is that they both have to deal with variables and I use the Tradition method and the DISTRIBUTIVE PROPETY in oder to solve them. Also I divide, add, and subtract all throughout the problem.
The difference between the two eqautions is..... (as I stated before) one equation ends with a product of negative number and the other with a postivie.
To get the value of the first eqaution I first had to subract 7T form each side then subtract 18 from eah side and then divide it by 3. For the Problem B I subtracted 7u from both sides and then added 7 to both sides. After that I divided both of what was left by 7. So basically I did the same thing with both problems but with different numbers.
****I explained up above the strategy I use (Distrubitive property and the traditional method.) and the explaination to how I solved this problem. *****
I do not believe there is another efficent way to solve this problem because it would be extremly difficult and not as *FUN* as it should be and of course we all know.....MATH IS FUNN!!!*
I thought these problems were easy and extremly fun a math filled!
Kellsie mitchell
ReplyDeletemath-3
problem 1-7t=10t+18 t=6
problem 2 I found the answer by subtracting 18 from each side and then i subtracted each by 7. and the i divided each side by 3 and my answer came out to six. Ther are different way to do this i did it this waty because it seemed to be the easiest way.
14u – 7 = -14 – 7u
i found the answer by adding 7 to each side. then i divided each side by 14 and i got left with u=-14u. next i brought down the other negative and that made two negatives and two negatives equal a postive. so u=14. There are other ways to do this problem u van divide first but it is harder that is y i did it the easier way.
problem 4 equation a i subtracted first and equationb i added first. the i dived both of them and equation a i divided again.
Alex Ramos
ReplyDeleteMath 3
7t = 10t + 18
Reorder the terms:
7t = 18 + 10t
Move all terms containing t to the left, all other terms to the right.
Add '-10t' to each side of the equation.
7t + -10t = 18 + 10t + -10t
Combine like terms: 7t + -10t = -3t
-3t = 18 + 10t + -10t
Combine like terms: 10t + -10t = 0
-3t = 18 + 0
-3t = 18
Divide each side by '-3'.
t = -6
14u + -7 = -14 + -7u
Reorder the terms:
-7 + 14u = -14 + -7u
Move all terms containing u to the left, all other terms to the right.
Add '7u' to each side of the equation.
-7 + 14u + 7u = -14 + -7u + 7u
Combine like terms: 14u + 7u = 21u
-7 + 21u = -14 + -7u + 7u
Combine like terms: -7u + 7u = 0
-7 + 21u = -14 + 0
-7 + 21u = -14
Add '7' to each side of the equation.
-7 + 7 + 21u = -14 + 7
Combine like terms: -7 + 7 = 0
0 + 21u = -14 + 7
21u = -14 + 7
Combine like terms: -14 + 7 = -7
21u = -7
Divide each side by '21'.
u = -1/3
The resemblence between the two problems is that -1/3 is 1/18 of -6. I think this problem couldve been harder if there were more operations used and if the numbers weren't so easily divide.
Mae-Lin L. Math:2
ReplyDelete7t=10t+18
-6t -6t
t=4t+18
-4t -4t
-3t=18
3 3
t=6
First I wrote the equation. Second I subtracted 6t. After it equaled to t=4t+18. Then I subtracted 4t and I got -3t=18. Lastly I divided by 3 and I got t=6
14u-7=14-7u
+7 +7
14u=21-7u
-7u -7u
7u=21
7 7
u=3
First I wrote the equation. Second I added 7 and I got 14u=21-7u. Then I subtracted 7u and it came out to be 7u=21. Lastly I divided by 3 and got for an answer u=3.
equation 1; I did the traditonal math and got t=(-6) i did this because it is the least hardest way to figure this out and that is what we have been learning in class. for the second one i did the same thing and got u=(-1)
ReplyDeletethey were both the same by ending in a negitive number.
Austin Daniels class;2
number1 the first variable is -6=t. the second variable is -1=u. i did tarditional math because thats what im best at. The same was that they both ended up being negative numbers. they are diffrent because it is a different letter. Tyler Daniels class4
ReplyDeleteBrittany Kozakiewicz Blog# 5 Math: 2
ReplyDeleteThe first thing I did was write down the first equation which was 7t=10t+18. Then I subtracted by 6t and it came out to t = 4t + 18. After I got that I subtracted by 4t and got -5t = 18. Next I divided by 3, finally got t = .6
Then I did the second equation, which is 14u + 7= 14-7u. To start off I added seven and got 14u = 21-7u. Next I subtracted 7u, and got 7u = 21. To finish I divide by 7 and got
U = 3. They both came out to do different answers. I had to subtract seven from both of them. I didn’t have a lot of problems, because I do this kind of stuff for home work and in class. I have done this in the 7th grade for homework and for class work.
Alicia Dugan class 4
ReplyDelete7t=10t+18
the first step you have to do is is add ten T to both sides of the equation and then from there you have seventeen t on one side and then you have eight teen on the other side. the next step is subtract seven teen from both sides and then you are left with variable t=one and that's your answer for part a.
14u-7=14-7u
the first thing you have to do is is take away seven u from both sides and then you get seven u minus seven on one side and then you get four teen on the other side. after that you subtract seven from both sides and then you are left with seven u and seven. last thing you have to do is divide seven from both sides and then the answer you get is u=one
Name: Jessica S.
ReplyDeleteClass:Math:1
1. 7t=10t+18 14u-7=(-14)-7u
t=(-6) u=(-3)
2. What i did to solve this problem is that I used the traditional method. For the first equation 7t=10t+18 i got t=(-6) because i first subtracted 10t to both sides and got -3t=18 so then I divided those 2 numbers by -3t and got t=(-6). For the second equation that i had to solve was 14u-7=(-14)-7u and I got the answer u=(-6). I first subtracted 7u to bothe sides by the number that was being multiplied by the variable. Then I added 7 to 7 and -14 and got 7u=(-21). After that I divided both of those numbers by 7 and I got u=(-6).
3. Well i worked out the problem with the traditional method on some scrap paper and i did all my math and look at my notes just incase i forgot how to do a problem like this. So i got my answers then i checked on a calculater to see if i got the answers right.
4.One thing that was the same about both was that both variables equaled a negative number.One thing that was different about them was that the both got different answers when i replaced the variable with its number. One of the things i had to do differently was that when 14u-7=(-14)-7 turned into 7u-7=(-14) i had to add but for 7t=10t=18 i had to subtract.
* There wasnt really another way to solve this problem.
* I thought this problem was hard at first but then it got a little easier when i went on to solve it until i got the right answer for each variable.
Caroline B
ReplyDeleteClass 1
1. Equation 1 is 7t = 10t +18
And how I solved is in 4 simple steps.
Step 1
I switched the arrangement of them and came to
10t + 18 = 7t
Step 2
I subtracted 7 from 7 and 10
3t + 18 = 0t
Step 3
I subtracted 0 from 0 and 18 and got the same equation as above.
Step 4
I divived 18 by 3 and 3 by 3 and I got the answer T=6
Equation 2 was 14u-7=(-14)- 7u
I answered this equation in 3 simple steps.
Step 1
I subtracted 7 on both sides
Step 2
I subtracted 7 again on both sides
Step 3
I divided both 7's by 7 and got the answer u=1
3. I did these steps becuase I can understand them better.
4.The methods in which I solved them were the same. They both have 7's in them. For equation A they don't give a full equation only have, and equation B has 2 full equations. Equation B has a negative number the other one doesn't. The first one I hasd to switch but then after that I used the same method for both of them.
Comments and Thoughts
I like this blog because it was easy and it was great review for the test that class 1 has to take. I thought that A was a little confusing but when I turned it around I understood it alot better.