# EquationCalculate x from (2x+3)/3 + (x-1)/2 = (-x+3)/6 .

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You should transfer all fractions to the left side such that:

Notice that only numerator could be zero such that:

Since 8!=0,then only x could be 0.

Hence, evaluating the solution to the given equation yields

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We have to determine x given (2x+3)/3 + (x-1)/2 = (-x+3)/6

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

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

=> 4x + 6 + 3x - 3 = -x + 3

=> 7x + 3 = -x + 3

=> 6x = 0

=> x = 0

The required solution is x = 0

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First thing, to determine x, we'll have to calculate the least common denominator of the 3 ratios.

LCD = 2*3

LCD = 6

Now, we'll multiply the first ratio by 2 and the second ratio by 3. The 3rd ratio has the denominator 6, so it won't be multiplied.

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

We ca re-write the expression without denominator:

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

We'll remove the brackets:

4x + 6 + 3x - 3 = -x + 3

We'll move the terms from the right side to the left side:

4x + 6 + 3x - 3 + x - 3 = 0

We'll combine and eliminate like terms:

8x = 0

We'll divide by 8:

x = 0

The solution of the equation is x = 0.