4/8(2.7m-2,1/4n)-4.2(5/7m-0.5n)

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To simplify the expression, we will first distribute the coefficients:

4/8(2.7m - 2) - 4.2(5/7m - 0.5n)

= 0.5(2.7m - 2) - 4.2(5/7m - 0.5n)

Next, we will simplify the expression by multiplying and combining like terms:

0.5(2.7m - 2) - 4.2(5/7m - 0.5n)

= 0.52.7m - 0.52 - 4.25/7m + 4.20.5n
= 1.35m - 1 - 3m + 2.1n
= -1.65m + 2.1n - 1

Therefore, the simplified expression is -1.65m + 2.1n - 1.