Bài 25 trang 111 SBT Toán Đại số 10 : Giải các bất phương trình sau...

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} ight.;)

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} ight..)

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} ight. Leftrightarrow left{ matrix{
– 30x + 9 > 10x – 35 hfill cr
2x – 1 < 15x – 5 hfill cr} ight. cr
& Leftrightarrow left{ matrix{
– 40x > – 44 hfill cr
– 13x < – 4 hfill cr} ight. Leftrightarrow left{ matrix{
x < 1,1 hfill cr
x > {4 over {13}} hfill cr} ight. cr} )

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} ight. 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} ight. cr
& Leftrightarrow left{ matrix{
{9 over 4}x le {{13} over {12}} hfill cr
{{22} over {15}} > {7 over 5}x hfill cr} ight. Leftrightarrow left{ matrix{
x le {{13} over {27}} hfill cr
x < {{22} over {21}} hfill cr} ight. Leftrightarrow x le {{13} over {27}} cr} )

Đáp số (x le {{13} over {27}})