Solve each equation. Express fraction answers in lowest terms. Check each solution. Am I Right? If not please explain where I went wrong and please explain how you solved this step by step line by line and show your work. I am getting confussed on ow you put some asnwers in fraction form and when do you do that? I will really appreciate your help!!!
a) 3h + 4 = 6
(I am just making sure does h = 0.66?)
b) 5k - 3 = -2
(I am making sure is the answer k = 0.2?)
c) -7w + 2 = -3
(I am just making sure is the answer w = 0.714?)
d) -4d-3= -1
(Is the answer -0.75?)
e) 5t - 4= 3
(Is the answer t= 1.4)
Solve each equation. Express fraction answers in lowest terms. Check each solution. Am I Right?
Your answers are correct. However, what I think you are doing is using a calculator to do the arithmetic.
For example:
a) 3h + 4 = 6 -4 from both sides
3h = 2 Then divide by 3. You are putting 2/3 into the calculator. Fractionally - the answer is 2/3 (two thirds) or two over three.
Go back through your problems. Rather then putting that last calculation into the calculator, just express it as a fraction.
b) 5k - 3 = -2
5k = 1
k = 1/5
Often times when solving equations - that solution is then put back into another equation. A decimal answer may not help us since often times we round or do other things with the decimal. When solving equations, if the answer doesn't come out "even", leave it in fractional form.
Reply:First, and this is between yourself and your teacher, the problem asked for fractions to be in lowest form, but you answered in decimals. Perhaps, you should rewrite your answer as fractions, such as, a) h = .66 as h = 2/3.
a, b, and c look correct, except as noted above.
d should be -1/2
e looks ok, except as noted above t = 1 2/5
Reply:a) b = 2/3 = .66 (correct!)
b) k = 1/5 = 0.2 (correct!)
c) w = 5/7 ≈ 0.714 (correct!)
d) d = -(2/4) = -(1/2) = -0.5 (CHECK)
Remember, the instructions state that you need to express each fraction in lowest terms. Lets take a closer look:
-4d - 3 = -1
-4d = -1 + 3
-4d = 2
d = -(2/4) ===simplify====%26gt; d = -(1/2) = -0.5 (%26lt;==ANSWER!)
e) t = 7/5 = 1.4 (correct!)
Great job!! I know you're seeing the answers as: "Now, divide one by five" and you punch that into your calculator to get your decimal answer. Think about it. If you say: "Divide one by five", you can write a fraction: 1 divided by 5 ==%26gt; 1 / 5 ==%26gt; 1/5
Hope I helped!
Reply:a) 3h=2
h=2/3
.66666666 repeating u were right
b) 5k=1
k=0.2 you were right
c) -7w=-5
w=5/7
0.714 you were right
d) -4d=2
d= -0.5
e) 5t=7
t=7/5
t=1.4 you were correct
hope this helps!
Reply:a) nope, need to round, it is .67
b) ya
c) ya
d) nope, it is -.25
e) ya
Reply:All are correct.
Reply:Q. A:
3h + 4 = 6
1. Place all constants on one side of the equation and all variables on the other side of the equation; variables are the values that change, they have a letter and a coefficient. Constants do not have letters next to them and remain the same, that is why they are called constants.
So ....... 3h + 4 = 6 becomes:
3h = 6 - 4
Notice that when you move a value from one side of the equation to another, the sign chages. In this case, the sign changed fomr positive to negative. This is so that the + 4 can be cancled. 3h = 6 - 4 is the simplified form of writing:
3h + 4 - 4 = 6 - 4
What you do to one side of the equation, you must do to the other. To get the negative 4 on the opposite side of the equation, we have to cancel the positive 4 on the other side. Positive and negative cancel each other, leaving a value of zero. 3h + 0 = 6 - 4 written: 3h = 6 - 4.
2. We can further simplify the expression 3h = 6 - 4 by adding like terms, ie constants with constants and variables with variables. Positive 6 minus 4 -- minus because the 4 is negative -- gives a value of positive 2. The 2 is positive because the larger number is positive. The simplified expression is:
3h = 2
3. We can further simplify the expression by dividing both sides by 3 or multiplying both sides by (1/3). This gives h a coefficient of positive 1, hence the value of h.
(1/3)(3h) = (1/3)(2)
h = 2/3
h = 0.6666666667
h = 0.67 -- 2 sig. figures --
--------------------------------------...
Q. B
5k - 3 = - 2
1. First move all constants to one side of the equation and all variables to the other side of the equation.
5k = - 2 + 3
The sign again changes, but this time from negative to positive. What was done was........
5k - 3 + 3 = - 2 + 3
What you do to one side of the equation you do to the other side of the equation. Positive 3 was added to both sides of the equation, so as to eliminate the negative 3. The simplified expression is:
5k = - 2 + 3
2. Further simplify the expression by adding like terms, ie constants with constants and variables with variables:
5k = 1.
The 1 is positive because the larger number is positive.
3. Further simplification can be done, by dividing both sides by 5 or multiplying by (1/5). This gives k a coefficient of positive 1 and hence the value of k.
(1/5)(5k) = (1)(1/5)
k = 1/5
k = 0.2
--------------------------------------...
Q. C
- 7w + 2 = - 3
1. First put all constants to one side of the equation and all variables on the other side of the equation.
- 7w = - 3 - 2
2. Add like terms ie constants with constants and variables with variables
- 7w = - 5
Note: adding two negative numbers, is like adding two positive numbers, except there is a negative sign infront of the number.
3. Divide both sides of the equation by - 7 or multiply both sides by ( - 1/7) so that w has a new coefficient of positive 1. Note, in this case, we have to multiply or divide by a negative number, so that the variable has a positive coefficient of 1.
( - 1/7)(- 7w) = (- 1/7)(- 5)
w = 5/7
w = 0.7142857143
w = 0.71 -- 2 sig. figures --
Note: a negative multiplied by a negative gives a positive
----------------------------------
Q. D -- TT_TT sry hun, but I think you got this one wrong ! --
- 4d - 3 = - 1
1. Place all constants on one side of the equation and all variables on the other side of the equation.
- 4d = - 1 + 3
2. Add like terms, ie constants with constants and variables with variables.
- 4d = 2
3. Divide both sides of the equation by negative 4 of multiply both sides of the equation by negative (1/4); the negative sign will cancel out the negative sign, and make the new coefficient of d, positive 1, giving the value of d.
( - 1/4)(- 4d) = (- 1/4)(2)
d = - 2/4
d = - 1/2
d = - 0.5
--------------------------------------...
Q. E
5t - 4 = 3
1. Place all constants to one side of the equation and all variables on the other side of the equation.
5t = 3 + 4
2. Add like terms, ie constants with constants and variables with variables.
5t = 7
3. Divide both sides of the equation by positive 5 or multiply both sides by positive (1/5). This gives t a new coefficient of positive 1, hence the value of t.
(1/5)(5t) = (7)(1/5)
t = 7/5
t = 1.4
--------------------------------
PROOF:
To ensure that you have the correct answers, you can subsitute the values into the equations:
Example:
Using the first expression: 3h + 4 = 6,
and the value of h as 2/3 or 0.67
Subsitute 2/3 for h
3h + 4 = 6
3(2/3) + 4 = 6 -- 3's cancel --
2 + 4 = 6
6 = 6
The answer is correct ! you can do these for the other values, to ensure that they are correct
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