Question

Решите систему неравенств: 1) {x> 1, x> 2,5; 2) {- 2x <-3, x <3; 3) {x <1,5, x> -2; 4) {4-5x> -1,1 / 6x <2; 5) {0,6x> 9,1 / 3x <2; 6) {9x> 0,1 / 7x> -1. Смотреть ответ tansykpayevazhanel tansykpayevazhanel Ответ:вотПошаговое объяснение:понасльжпчыо

Answer 1

Solution to the System of Inequalities:

To solve the given system of inequalities, let's solve each inequality separately and then find the intersection of the solution sets.

1) {x > 1, x > 2.5}: - The first inequality, x > 1, represents all values of x greater than 1. - The second inequality, x > 2.5, represents all values of x greater than 2.5. - Taking the intersection of these two solution sets, we find that x > 2.5.

2) {-2x < -3, x < 3}: - The first inequality, -2x < -3, can be rewritten as x > 3/2. - The second inequality, x < 3, represents all values of x less than 3. - Taking the intersection of these two solution sets, we find that x > 3/2.

3) {x < 1.5, x > -2}: - The first inequality, x < 1.5, represents all values of x less than 1.5. - The second inequality, x > -2, represents all values of x greater than -2. - Taking the intersection of these two solution sets, we find that -2 < x < 1.5.

4) {4-5x > -1.1, 6x < 2}: - The first inequality, 4-5x > -1.1, can be rewritten as x < 1.42. - The second inequality, 6x < 2, represents all values of x less than 1/3. - Taking the intersection of these two solution sets, we find that x < 1/3.

5) {0.6x > 9.1, 3x < 2}: - The first inequality, 0.6x > 9.1, can be rewritten as x > 15.17. - The second inequality, 3x < 2, represents all values of x less than 2/3. - Taking the intersection of these two solution sets, we find that x > 15.17.

6) {9x > 0.1, 7x > -1}: - The first inequality, 9x > 0.1, can be rewritten as x > 0.011. - The second inequality, 7x > -1, represents all values of x greater than -1/7. - Taking the intersection of these two solution sets, we find that x > 0.011.

Final Solution:

The solution to the given system of inequalities is: - x > 2.5 - -2 < x < 1.5 - x < 1/3 - x > 15.17 - x > 0.011

Please note that these solutions are based on the given inequalities and their intersections.