Đáp án:
$\begin{array}{l}
1)\\
a)\left( {3,1 - 2,5} \right) - \left( { - 2,5 + 3,1} \right)\\
= 3,1 - 2,5 + 2,5 - 3,1\\
= 0\\
b) - \left( {251.3 + 281} \right) + 3.551 - \left( {1 - 281} \right)\\
= - 3.251 - 281 + 3.551 - 1 + 281\\
= 3.\left( {551 - 251} \right) + \left( { - 281 + 281} \right) - 1\\
= 3.300 - 1\\
= 900 - 1\\
= 899\\
c) - \left( {\dfrac{3}{5} + \dfrac{3}{4}} \right) - \left( { - \dfrac{3}{4} + \dfrac{2}{5}} \right)\\
= - \dfrac{3}{5} - \dfrac{3}{4} + \dfrac{3}{4} - \dfrac{2}{5}\\
= - \dfrac{3}{5} - \dfrac{2}{5} = - \dfrac{5}{5} = - 1\\
2)\\
\left| a \right| = 1,5 \Rightarrow \left[ \begin{array}{l}
a = 1,5\\
a = - 1,5
\end{array} \right.\\
\left| b \right| = 0,75 \Rightarrow \left[ \begin{array}{l}
b = 0,75\\
b = - 0,75
\end{array} \right.\\
+ Khi:a = 1,5;b = 0,75\\
M = a:2 - 3:b\\
= 1,5:2 - 3:0,75 = - 3,25\\
+ Khi:a = - 1,5;b = 0,75\\
\Rightarrow M = a:2 - 3:b\\
= - 1,5:2 - 3:0,75 = - 4,75\\
+ Khi:a = 1,5;b = - 0,75\\
\Rightarrow M = a:2 - 3:b\\
= 1,5:2 + 3:0,75 = 4,75\\
+ Khi:a = - 1,5;b = - 0,75\\
\Rightarrow M = a:2 - 3:b\\
= 3,25\\
3)\\
Do:\left| a \right| + \left| b \right| \ge \left| {a + b} \right|\\
A = \dfrac{{ - 3}}{8} + \left| {\dfrac{3}{5} - 2x} \right|\\
\left| {\dfrac{3}{5} - 2x} \right| \ge 0 \Rightarrow A \ge - \dfrac{3}{8}\\
\Rightarrow GTNN:A = - \dfrac{3}{8}\\
Khi:\dfrac{3}{5} = 2x \Rightarrow x = \dfrac{3}{{10}}\\
B = \left| {\dfrac{3}{8} - 2x} \right| + \left| {2x + \dfrac{1}{3}} \right| \ge \left| {\dfrac{3}{8} - 2x + 2x + \dfrac{1}{3}} \right|\\
\Rightarrow B \ge \dfrac{{17}}{{24}}\\
\Rightarrow GTNN:B = \dfrac{{17}}{{24}}\\
C = \left| {3x - \dfrac{1}{5}} \right| + \left| {3x - 2} \right|\\
= \left| {3x - \dfrac{1}{5}} \right| + \left| {2 - 3x} \right| \ge \left| {3x - \dfrac{1}{5} + 2 - 3x} \right|\\
\Rightarrow C \ge \dfrac{9}{5}\\
\Rightarrow GTNN:C = \dfrac{9}{5}
\end{array}$
