Giải các bất phương trình sau:
a) \(\left\{ \matrix{
- 2x + {3 \over 5} > {{2x - 7} \over 3} \hfill \cr
x - {1 \over 2} < {{5(3x - 1)} \over 2} \hfill \cr} \right.;\)
b) \(\left\{ \matrix{
{{3x + 1} \over 2} - {{3 - x} \over 3} \le {{x + 1} \over 4} - {{2x - 1} \over 3} \hfill \cr
3 - {{2x + 1} \over 5} > x + {4 \over 3} \hfill \cr} \right..\)
Gợi ý làm bài
\(\eqalign{
& \left\{ \matrix{
- 2x + {3 \over 5} > {{2x - 7} \over 3} \hfill \cr
x - {1 \over 2} < {{5(3x - 1)} \over 2} \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
- 30x + 9 > 10x - 35 \hfill \cr
2x - 1 < 15x - 5 \hfill \cr} \right. \cr
& \Leftrightarrow \left\{ \matrix{
- 40x > - 44 \hfill \cr
- 13x < - 4 \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
x < 1,1 \hfill \cr
x > {4 \over {13}} \hfill \cr} \right. \cr} \)
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Đáp số: \({4 \over {13}} < x < 1,1.\)
b)
\(\eqalign{
& \left\{ \matrix{
{{3x + 1} \over 2} - {{3 - x} \over 3} \le {{x + 1} \over 4} - {{2x - 1} \over 3} \hfill \cr
3 - {{2x + 1} \over 5} > x + {4 \over 3} \hfill \cr} \right. \cr
& \Leftrightarrow \left\{ \matrix{
{3 \over 2}x + {x \over 3} - {x \over 4} + {2 \over 3}x \le {1 \over 4} + {1 \over 3} - {1 \over 2} + 1 \hfill \cr
3 - {1 \over 5} - {4 \over 3} > x + {2 \over 5}x \hfill \cr} \right. \cr
& \Leftrightarrow \left\{ \matrix{
{9 \over 4}x \le {{13} \over {12}} \hfill \cr
{{22} \over {15}} > {7 \over 5}x \hfill \cr} \right. \Leftrightarrow \left\{ \matrix{
x \le {{13} \over {27}} \hfill \cr
x < {{22} \over {21}} \hfill \cr} \right. \Leftrightarrow x \le {{13} \over {27}} \cr} \)
Đáp số \(x \le {{13} \over {27}}\)