how do you solve this?

Question

(1/6) - (x/3) = (x-3) / (2)

don't you have to get the denominators the same first?
thanks for the help.

Answer 1

(1/6) - (2x/6) = (x-3)/2

(1-2x)/6 = (x-3)/2

Cross multiply :

(1-2x)2 = 6(x-3)

2-4x = 6x-18

2 = 10x - 18

20 = 10x

ANSWER : x=2

Answer 2

How about this:
1/6 - x/3 = (x-3)/2
2/6 - 2x/3 = x-3
x + 2x/3 = 3 + 2/6
x(1 + 2/3) = 3 + 1/3
x = (3+1/3) / (1 + 2/3)
x = (1 + 1 + 1 + 1/3) / (1 + 2/3)
x = (1 + 1 + 3/3 + 1/3) / (1 + 2/3)
x = (1 + 1 + 2/3 + 2/3) / (1 + 2/3)
x = ((1 + 2/3) + (1 + 2/3)) / (1 + 2/3)
x = (2 (1 + 2/3) ) / (1 + 2/3)
x = 2

So, answer to your question is no, you don't necessary need to get the denominators the same first.

Answer 3

The lowest common denominator is 6.
Multiply everything by 6
6(1/6) - 6(x/3) = 6(x-3)/2
Simplify
1 - 2x = 3(x-3)
Simplify again
1 - 2x = 3x - 9
Add 2x to each side
1 = 5x - 9
Add 9 to each side
10 = 5x
Divide both sides by 5
2 = x
Answer: x = 2

Answer 4

Solve,

(1 / 6) - (x / 3) = (x - 3) / (2)

Multiply both sides by 6,

6(1 / 6) - 6(x / 3) = 6(x - 3) / (2)

Simplify,

1 - 2x = 3(x - 3)

1 - 2x = 3x - 9

1 + 9 = 3x + 2x

5x = 10

x = 10 / 5

x = 2

Answer 5

Yes, so the LCD is 6. Multiply each term by 6 to get:


(6x1)/6 - 6(x/3) = 6(x-3)/2 by cancellation you get:

1 - 2X = 3(x-3) distribute

1 - 2X = 3x-9 add 2x to both sides
+ 2x +2x
__________________________

1 = 5x -9 add 9 to both sides

+9 +9
_____________________


10 =5x divide both by 5

2 =x

prove by substituting the 2 in place of x

1/6 -2/3 = (2-3)/2 change to LCD
1/6 - 4/6 = -1/2
-3/6 = -1/2 reduce first fraction
-1/2 = -1/2

Therefore, x = 2

Answer 6

It may be easiest to get id of the denominators entirely by multiplying both sides by six. This gives you:

1-2x=3x-9

10=5x

2=x

Answer 7

If you are adding or subtracting you need common denominators BUT if you are just mult/dividing than you do not need common denominators.