(2x-3)/12-(5x-11)/2=(x+3)/6-(x+2)/3

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вопрос

To solve this equation, we first need to combine like terms on both sides and then simplify.

Starting with the left side of the equation:

(2x-3)/12 - (5x-11)/2
= (2x-3)/12 - 6(5x-11)/12
= (2x - 3 - 30x + 66) / 12
= (-28x + 63) / 12
= -28x/12 + 63/12
= -7x/3 + 21/4

Now, simplifying the right side of the equation:

(x+3)/6 - (x+2)/3
= 2(x+3)/12 - 4(x+2)/12
= (2x + 6 - 4x - 8) / 12
= (-2x - 2) / 12
= -2(x+1) / 12
= -2x/12 - 2/12
= -x/6 - 1/6

Now we set the two sides equal to each other and solve for x:

-7x/3 + 21/4 = -x/6 - 1/6

First, let's get rid of the fractions by multiplying everything by 12:

-28x + 63 = -2x - 2

Now, add 2x to both sides and subtract 63 from both sides:

-26x = -65
x = -65 / -26
x = 5/2

Therefore, the solution to the equation is x = 5/2 or x = 2.5.