6/23- 1/3 ×1/3/4+1/4 - 6>0

To solve the inequality, let's simplify the expression: 6/23 - 1/3 × 1/3/4 + 1/4 - 6 > 0

First, let's simplify the fractional multiplication: 6/23 - 1/3 × 1/3/4 + 1/4 - 6 = 6/23 - 1/3 × 1/12 + 1/4 - 6 = 6/23 - 1/36 + 1/4 - 6

Now, let's common denominators: = 6/23 - 1/36 + 9/36 - 6 = 6/23 + 8/36 - 6

Next, let's find a common denominator and combine the fractions: = 6/23 + 2/9 - 6 = (6/23) + (2/9) - (54/9) = 6/23 + 2/9 - 54/9

Now, let's find a common denominator again and combine the fractions: = (6/23) + (2/9) - (54/9) = (6/23) + (2/9) - (207/9)

Next, find a common denominator and combine the fractions: = (6/23) + (2/9) - (207/9) = (6/23) + (2/9) - (207/9) * (23/23) = (6/23) + (2/9) - (4761/207)

Now, let's find a common denominator and combine the fractions: = (6/23) + (2/9) - (4761/207) = (6/23) + (2/9) - (4761/207) * (9/9) = (6/23) + (2/9) - (42849/1863)

Finally, let's find a common denominator and simplify the expression further: = (6/23) + (2/9) - (42849/1863) = (11118/50907) + (9838/50907) - (42849/1863) = (11118 + 9838 - 42849) / 50907 = (-2193/50907)

Therefore, the simplified expression is -2193/50907.

To determine whether -2193/50907 is greater than zero or not, we can simply check if the numerator (-2193) is less than zero. Since -2193 is less than zero, that means -2193/50907 is also less than zero.

Hence, the inequality 6/23 - 1/3 × 1/3/4 + 1/4 - 6 > 0 is not true.