Solve:
E = 1/2mv^2
Please explain it for me?
And this other one:
Clear the fractions. Do NOT solve:
(1/3)x + (1/12)x = (3/4)x - 2
and in addition to that, there's a question after that that says:
In the above problem, why did you also have to multiply the last number by 12?
Please explain! Thanks!
E = 1/2mv^2
Please explain it for me?
And this other one:
Clear the fractions. Do NOT solve:
(1/3)x + (1/12)x = (3/4)x - 2
and in addition to that, there's a question after that that says:
In the above problem, why did you also have to multiply the last number by 12?
Please explain! Thanks!
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Solve for m:
E = 1/2mv²
mv² = 2E
m = 2E/v²
Solve for v:
v² = 2E/m
v = ± √(2E/m)
Answer: m = 2E/v²; v = ± √(2E/m)
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1/3x + 1/12x = 3/4x - 2
4x + x = 9x - 24
4x = 24
x = 6
Answer: x = 6; we multiply all numbers (not only the last) by 12 to eliminate the nitty-gritty of dealing with fractions. If we solve without multiplying each item by 12, the result will be the same.
1/3x + 1/12x = 3/4x - 2
(4x + x)/12 = (3x - 8)/4
5x/12 = (3x - 8)/4 cross multiply
4(5x) = 12(3x - 8)
20x = 36x - 96
16x = 96
x = 6
But you will notice that it more cumbersome than just multiply each item by their LCM which is 12.
Check:
1/3(6) + 1/12(6) = 3/4(6) - 2
2 + 0.5 = 4.5 - 2
2.5 = 2.5
E = 1/2mv²
mv² = 2E
m = 2E/v²
Solve for v:
v² = 2E/m
v = ± √(2E/m)
Answer: m = 2E/v²; v = ± √(2E/m)
-----------
1/3x + 1/12x = 3/4x - 2
4x + x = 9x - 24
4x = 24
x = 6
Answer: x = 6; we multiply all numbers (not only the last) by 12 to eliminate the nitty-gritty of dealing with fractions. If we solve without multiplying each item by 12, the result will be the same.
1/3x + 1/12x = 3/4x - 2
(4x + x)/12 = (3x - 8)/4
5x/12 = (3x - 8)/4 cross multiply
4(5x) = 12(3x - 8)
20x = 36x - 96
16x = 96
x = 6
But you will notice that it more cumbersome than just multiply each item by their LCM which is 12.
Check:
1/3(6) + 1/12(6) = 3/4(6) - 2
2 + 0.5 = 4.5 - 2
2.5 = 2.5
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E = (1/2) m v^2 ==> 2E = m v^2 ==> v^2 = 2E / m ==> v = (2E/m)^(1/2)
(1/3) x + (1/12) x = (3/4) x - 2
To clear the fractions consider the numbers in the denominators of the different terms.
The numbers are 3, 12, and 4. Their L.C.M. is 12
If we multiply both sides by 12 the fractions will be cleared. The eqn after multiplication becomes
4x + x = 9x - 24 Now you can solve it.
An equation has 2 sides. Whatever operation we perform on the left side the same operation
must be performed on the right side of the equality sign to keep both sides equal.
Multiply both sides by 12 means each term on the left side as well as each term on the right side
should be multiplied by 12. Since the last number is a term on the right side it should also be
multiplied by 12.
(1/3) x + (1/12) x = (3/4) x - 2
To clear the fractions consider the numbers in the denominators of the different terms.
The numbers are 3, 12, and 4. Their L.C.M. is 12
If we multiply both sides by 12 the fractions will be cleared. The eqn after multiplication becomes
4x + x = 9x - 24 Now you can solve it.
An equation has 2 sides. Whatever operation we perform on the left side the same operation
must be performed on the right side of the equality sign to keep both sides equal.
Multiply both sides by 12 means each term on the left side as well as each term on the right side
should be multiplied by 12. Since the last number is a term on the right side it should also be
multiplied by 12.
-
(1/3)x + (1/12)x = (3/4)x – 2
x/3 + x/12 = 3x/4 – 2
x/3 + x/12 – 3x/4 + 2 = 0
Multiply each number by the common denominator of 12
12(x/3) + 12(x/12) - 12(3x/4) + 12(2) = 0
4x + x - 9x + 24 = 0
-4x + 24 = 0
4(-x + 6) = 0
You had to multiply the last number by 12 because that was the common denominator. What you do to one number, you have to do to all numbers.
x/3 + x/12 = 3x/4 – 2
x/3 + x/12 – 3x/4 + 2 = 0
Multiply each number by the common denominator of 12
12(x/3) + 12(x/12) - 12(3x/4) + 12(2) = 0
4x + x - 9x + 24 = 0
-4x + 24 = 0
4(-x + 6) = 0
You had to multiply the last number by 12 because that was the common denominator. What you do to one number, you have to do to all numbers.