Answer:
c., d.
Step-by-step 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.
