Question

Which inequality is true for all real numbers? Check all that apply.

O a-b ac > bc
If a 2 b, then a + c2b+c
If c > 0, then a-c < a- d
If a

Answer 1

c., d.

Explanation:

a. Let a = 5; let b = -2

a - b < a + b

5 - (-2) < 5 + (-2)

5 + 2 < 5 - 2

7 < 3 this is a false statement, so choice a. is not true for all real numbers.

b. ac >= bc

Let a = 5; let b = 2; let c = -3

5(-3) >= 2(-3)

-15 >= -6 this is a false statement, so choice b. is not true for all real numbers.

c. If a >= b, then a + c >= b + c

You are adding the same amount, c, to both sides of a true inequality, so the result is still a rue inequality.

True

d. If c > d, then a - c < a - d

Start with c > d.

Multiply both sides by -1. Remember to flip the inequality sign.

-c < -d

Now add a to both sides.

a - c < a - d

True

e. If a < b, then a < b + c

Let a = 5, b = 7, and c = -5

If 5 < 7, then 5 < 7 + (-5).

If 5 < 7, then 5 < 2. This is a false statement.

Answer: c. and d. are true.