Question

(2x-5)/3-(5x-4)/2=(1-5x)/4+(5x+2)/6

Answer 1

$\dfrac{2x-5}{3}-\dfrac{5x-4}{2}=\dfrac{1-5x}{4}+\dfrac{5x+2}{6}\ \Big|\cdot 12\\\\\\4(2x-5)-6(5x-4)=3(1-5x)+2(5x+2)\\\\8x-20-30x+24=3-15x+10x+4\\\\-22x+4=-5x+7\\\\17x=-3\\\\x=-\dfrac{3}{17}$

Answer 2

To solve the equation, let's simplify it step by step.

Given equation:

(2x - 5)/3 - (5x - 4)/2 = (1 - 5x)/4 + (5x + 2)/6

First, let's find a common denominator for all the fractions involved. The common denominator is 12, which is the least common multiple of 3, 2, and 4.

Multiplying every term by 12 to clear the fractions:

12 * [(2x - 5)/3] - 12 * [(5x - 4)/2] = 12 * [(1 - 5x)/4] + 12 * [(5x + 2)/6]

Simplifying the equation:

4(2x - 5) - 6(5x - 4) = 3(1 - 5x) + 2(5x + 2)

8x - 20 - 30x + 24 = 3 - 15x + 10x + 4

Combine like terms:

-22x + 4 = -15x + 7

Now, let's isolate the variables on one side and constants on the other side:

-22x + 15x = 7 - 4

-7x = 3

Finally, solve for x by dividing both sides by -7:

x = 3 / -7

Therefore, the solution to the given equation is:

x = -3/7