Solution:

To solve the given expression, we need to follow the order of operations which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Therefore, let's simplify the expression step by step as follows:

Multiplication and Division
2/5 × (-3/7) = -6/35
-1/6 × 3/2 = -1/4
1/14 × 2/5 = 1/35

Addition and Subtraction
-6/35 - 1/4 + 1/35

Now, we need to find a common denominator to add or subtract the fractions.

Find the common denominator
The common denominator for 35 and 4 is 140. Therefore, we need to multiply each fraction by an appropriate form of 1 to create equivalent fractions with a common denominator of 140.

-6/35 × 4/4 = -24/140
-1/4 × 35/35 = -35/140
1/35 × 4/4 = 4/140

Addition and Subtraction
-24/140 - 35/140 + 4/140 = -55/140

Simplify the Fraction
-55/140 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 5.

-55/140 ÷ 5/5 = -11/28

Final Answer: -11/28

Therefore, the simplified form of 2/5×(-3/7)-1/6×3/2 1/14×2/5 is -11/28.

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