Question

Про числа а и b известно, что а < b.Из следующих неравенств выберите верное:1) а+2/3 < b+2/32) - а/5 < - b/53) а^3 > b^34) a-b >0Объясните как делать пожалуйста

Answer 1

Такие задачи решаются очень просто - нужно подставить числа в А и В
Тогда все становится на свои места. Например:
а<b
Допустим, что а = 9, а b=10, тогда
а+2/3  <  b+2/3 - вот это неравенство будет верным. И даже подставлять ничего не нужно. Потому, что к обеим частям неравенства прибавли одно и то же число. А когда к обеим частям неравенства прибавляют одно и то же число, значение не меняется.
Но подставить тоже всегда можно.

Answer 2

Solving the Inequalities

To solve the given inequalities and determine which ones are true, we can follow these steps:

1. Understand the Inequalities: - We have two numbers, a and b, where a is less than b.

2. Analyze Each Inequality: - Let's analyze each given inequality to determine which ones are true.

Analysis of the Inequalities

1. a + 2/3 < b + 2/3: - This inequality is not valid because adding the same value to both sides of an inequality does not change the inequality sign. Therefore, this inequality is always true regardless of the values of a and b.

2. -a/5 < -b/5: - This inequality is not valid because when we multiply or divide both sides of an inequality by a negative number, the inequality sign is reversed. Therefore, this inequality is always true regardless of the values of a and b.

3. a^3 > b^3: - This inequality is valid when a > b. However, since it's given that a < b, this inequality is not true in the given context.

4. a - b > 0: - This inequality is valid because it states that the difference between a and b is greater than 0, which is true given that a < b.

Conclusion

Based on the analysis, the only valid inequality is a - b > 0. This means that the difference between a and b is greater than 0, which aligns with the initial condition that a is less than b.