Question

Дано: -3а>-3b.сравнить1) a b2) 2/7a 2/7b3) b-4 a-44) -5/9b -5/9a5)3a+2 3b+26) -5a+10 -5b+10 пожалуйста с пояснением

Answer 1

-3а>-3b  ⇒ делим на (-3) и знак меняем на противоположный a < b

1) a< b
2) 2/7a< 2/7b   умножили верное неравенство a < b  на 2/7 - положительное число, знак неравенства не изменился
3) b-4 > a-4 
верное неравенство b > a  от обеих частей отняли поровну 4, знак неравенства не изменился
4) -5/9b < -5/9a
умножили верное неравенство  b < a   на(-5 /9 - отрицательное число, знак неравенства  изменился
5)3a+2 < 3b+2
Умножили верное неравенство
a < b  на 3 - положительное число, знак неравенства не изменился
и потом прибавили поровну число 2 и слева и справа
6) -5a+10> -5b+10
умножили верное неравенство a < b  на (-5) - отрицательное  число, знак неравенства  изменился
Потом прибавление к обеим частям неравенства 10 не меняет знак.

Answer 2

Comparing Expressions with Given Inequality

To compare the given expressions with the inequality -3a > -3b, we'll evaluate each expression and compare the results.

1) a + b: - We can't directly compare this expression with the given inequality. We need to simplify it further.

2) 2/7a + 2/7b: - We can simplify this expression by factoring out 2/7: (2/7)(a + b). - Since the inequality -3a > -3b can be divided by -3, it becomes a < b. Therefore, (2/7)(a + b) < 2/7b.

3) b - 4 + a - 4: - This expression simplifies to a + b - 8. - We can't directly compare this expression with the given inequality. We need to simplify it further.

4) -5/9b - 5/9a: - We can simplify this expression by factoring out -5/9: (-5/9)(b + a). - Since the inequality -3a > -3b can be divided by -3, it becomes a < b. Therefore, (-5/9)(b + a) < -5/9b.

5) 3a + 2 + 3b + 2: - This expression simplifies to 3a + 3b + 4. - We can't directly compare this expression with the given inequality. We need to simplify it further.

6) -5a + 10 - 5b + 10: - This expression simplifies to -5a - 5b + 20. - We can't directly compare this expression with the given inequality. We need to simplify it further.

Summary

After evaluating the given expressions, we can compare them to the inequality -3a > -3b as follows: - 2/7a + 2/7b < 2/7b - (-5/9)(b + a) < -5/9b

The other expressions need further simplification to directly compare them with the given inequality.