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

Answer 1

#x=-35#

#x-1# is common to both the terms in the left side of the equation.
Take #x-1# and write the remaining terms inside brackets:
#(x-1)(1/3-1/2)=6#

Proceed to solve the fractions enclosed in parenthesis:

#(x-1)((2-3)/6)=6#
#(x-1)(-1/6)=6#
#-(x-1)/6=6#
Next, multiply both sides by #-6#:
#-(x-1)/6color(red)(xx-6)=6color(red)(xx-6)#
#x-1=-36#
Add #1# to both sides:
#x-1color(red)(+1)=-36color(red)(+1)#
#x=-35#

Let's examine our resolution.

Plug in the value of #x=-35# in the given equation and solve:
Left side of the equation is #(x-1)/3-(x-1)/2#
#=(-35-1)/3-(-35-1)/2#
#=(-36)/3-(-36/2)#
#=-12-(-18)#
#=-12+18#
#=6=# right side of the equation.

Therefore, our answer is accurate.

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Answer 2

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

  1. Find a common denominator for the fractions, which in this case is 6.
  2. Rewrite the equation with the common denominator: (2(x-1) - 3(x-1))/6 = 6.
  3. Simplify the numerator: (2x - 2 - 3x + 3)/6 = 6.
  4. Combine like terms: (-x + 1)/6 = 6.
  5. Multiply both sides of the equation by 6 to eliminate the fraction: -x + 1 = 36.
  6. Subtract 1 from both sides: -x = 35.
  7. Multiply both sides by -1 to solve for x: x = -35.

Therefore, the solution to the equation (x-1)/3 - (x-1)/2 = 6 is x = -35.

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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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