Question

Какое из приведенных ниже неравенств не следует из неравенства х-у<z1) х-z-у<0, 2) у>х-z, 3) у<z-х , 4) z+у>х Подробное решение

Answer 1

тут просто надо переносить слагаемые в разные стороны. первое верно, т.к. z переносим с противоположным знаком. второе тоже верно. z перенесли влево, а у вправо и поменяли просто местами. четвертое верно. у перенесли вправо, х влево и поменяли местами стороны.

третье неверно. т.к. у>х-z

Answer 2

Analysis of the Given Inequalities

The given inequalities are: 1) x - z - y < 0 2) y > x - z 3) y < z - x 4) z + y > x

We need to determine which of the inequalities does not follow from the given set.

Solution

Let's analyze each inequality:

1) x - z - y < 0 2) y > x - z 3) y < z - x 4) z + y > x

To determine which inequality does not follow from the given set, we can manipulate the inequalities to see if they contradict each other.

From inequality 2, we can express y as: y = x - z

Substituting this value of y into inequality 1: x - z - (x - z) < 0 Simplifying, we get: -2z < 0 This inequality is always true, so it does not contradict the given set.

From inequality 3, we can express y as: y = z - x

Substituting this value of y into inequality 4: z + (z - x) > x Simplifying, we get: 2z > x This inequality is also always true and does not contradict the given set.

From inequality 4, we can express z as: z = x - y

Substituting this value of z into inequality 3: y < (x - y) - x Simplifying, we get: 2y < 0 This inequality is always true and does not contradict the given set.

Therefore, all the inequalities follow from the given set. There is no inequality that does not follow from the given set.

Conclusion

All the given inequalities follow from the set of inequalities provided.