Question

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

Answer 1

При решении использовал арифметические операции с дробями

Answer 2

To solve the equation 2/3(1/3x - 1/2) = 6x - 2(x - 1 1/4), you'll need to follow these steps:

1. Distribute and simplify on both sides of the equation: (2/3) * (1/3x - 1/2) = 6x - 2(x - 1 1/4)

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

2. Simplify the fractions on the left side: (2/9)x - (1/3) = 6x - 2x + 2(1 1/4)

3. Multiply both sides of the equation by the least common multiple (LCM) of the denominators to eliminate fractions. In this case, the LCM is 9: 9 * ((2/9)x - (1/3)) = 9 * (6x - 2x + 2(1 1/4))

   2x - 3 = 54x - 18 + 2(5/4)

4. Distribute on the right side and simplify: 2x - 3 = 54x - 18 + 5/2

5. Move like terms to opposite sides of the equation: 2x - 54x = -18 + 5/2 + 3

6. Combine like terms: -52x = -18 + 5/2 + 6/2

7. Add the fractions on the right side: -52x = (-36/2 + 5/2 + 6/2)

   -52x = -25/2

8. Divide by -52 to solve for x: x = (-25/2) / -52

9. Simplify the right side of the equation: x = (25/2) / 52

10. Reduce the fraction by dividing both the numerator and denominator by their greatest common divisor (which is 1): x = (25/2) / 52 x = 25 / (2 * 52) x = 25 / 104

So, the solution to the equation is: x = 25/104