Question

Given that 6 > -2, which statements are true? Check all that apply.

a) (2)(6) > (-2)(2)
b) 6/2 < -2/2
c) (-2)(6) > (-2)(-2)
d) 6/(-2) < -2/(-2)
e) (2)(6) < (-2)(2)
f) 6/2 > -2/2

Answer 1

The true statements, given that 6 is greater than -2, are (2)(6) > (-2)(2), (-2)(6) > (-2)(-2), and 6/2 > -2/2.

Step-by-step explanation:

The question asks which statements are true given that 6 is greater than -2. We need to evaluate the inequalities by applying the rules of multiplication and division for positive and negative numbers.

1. (2)(6) > (-2)(2): True, because both products are positive, and 12 is greater than -4.
2. 6/2 < -2/2: False, 6/2 is 3, and -2/2 is -1, so 3 is greater than -1.
3. (-2)(6) > (-2)(-2): True, because the product of two negative numbers is positive, and -12 is not greater than 4.
4. 6/(-2) < -2/(-2): True, because the division follows the same rules as multiplication, and -3 is less than 1.
5. (2)(6) < (-2)(2): False, the same case as the first statement, but the inequality sign is incorrect.
6. 6/2 > -2/2: True, as already stated, 3 is greater than -1.