How do you solve #1/6-x/2=(x-5)/3#?

Answer 1

see the entire solution process below:

First, multiple each side of the equation by #color(red)(6)# (the lowest common denominator of all the fractions) to eliminate the fractions while keeping the equation balanced:
#color(red)(6)(1/6 - x/2) = color(red)(6) xx (x - 5)/3#
#(color(red)(6) xx 1/6) - (color(red)(6) xx x/2) = cancel(color(red)(6))2 xx (x - 5)/color(red)(cancel(color(black)(3)))#
#(cancel(color(red)(6)) xx 1/color(red)(cancel(color(black)(6)))) - (cancel(color(red)(6))3 xx x/color(red)(cancel(color(black)(2)))) = 2(x - 5)#
#1 - 3x = 2x - 10#
Next, add #color(red)(3x)# and #color(blue)(10)# to each side of the equation to isolate the #x# term while keeping the equation balanced:
#1 - 3x + color(red)(3x) + color(blue)(10) = 2x - 10 + color(red)(3x) + color(blue)(10)#
#1 + color(blue)(10) - 3x + color(red)(3x) = 2x + color(red)(3x) - 10 + color(blue)(10)#
#11 - 0 = 5x - 0#
#11 = 5x#
Now, divide each side of the equation by #color(red)(5)# to solve for #x# while keeping the equation balanced:
#11/color(red)(5) = (5x)/color(red)(5)#
#11/5 = (color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5))#
#11/5 = x#
#x = 11/5#
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Answer 2

#x=11/5#

Eliminate the fractions in the equation by multiplying ALL terms on both sides of the equation by the #color(blue)"lowest common multiple"# ( LCM ) of the denominators 6, 2 and 3

For 6, 2, and 3, the LCM is 6.

Therefore, multiply every term by 6.

#(cancel(6)^1xx1/cancel(6)^1)-(cancel(6)^3xx x/cancel(2)^1)=(cancel(6)^2xx(x-5)/cancel(3)^1)#
#rArr1-3x=2(x-5)larr" no fractions"#

The bracket should be distributed to the right.

#rArr1-3x=2x-10#

Take 2x off of each side.

#1-3x-2x=cancel(2x)cancel(-2x)-10#
#rArr1-5x=-10#

Deduct one from each side.

#cancel(1)cancel(-1)-5x=-10-1#
#rArr-5x=-11#

Scoop out x by dividing both sides by -5.

#(cancel(-5) x)/cancel(-5)=(-11)/(-5)#
#rArrx=11/5#
#color(blue)"As a check"#

Enter this value into the equation; the solution is found if the left and right sides of the equation equal.

#"left side "=1/6-(11/5)/2=1/6-11/10=5/30-33/30=-28/30=-14/15#
#"right side"=(11/5-5)/3=(11/5-25/5)/3=(-14/5)/3=-14/15#
#rArrx=11/5" is the solution"#
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Answer 3

To solve the equation 1/6 - x/2 = (x-5)/3, we can follow these steps:

  1. Multiply every term in the equation by the least common denominator (LCD), which is 6. This gives us: 6 * (1/6) - 6 * (x/2) = 6 * ((x-5)/3)

  2. Simplify each term: 1 - 3x = 2(x-5)

  3. Distribute the 2 on the right side: 1 - 3x = 2x - 10

  4. Move all the x terms to one side and the constant terms to the other side: 1 + 10 = 2x + 3x 11 = 5x

  5. Divide both sides by 5 to solve for x: x = 11/5

Therefore, the solution to the equation 1/6 - x/2 = (x-5)/3 is x = 11/5.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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