Inequalities

Problem : What property is demonstrated by the following statement?
5 > 2 and 2 > 0 . Thus 5 > 0 .

Problem : If x is a positive real number, which inequality sign goes in the circle? What property does this show?
- x 0

Problem : If x and y are positive real numbers, which inequality sign goes in the circle?
x < y

Problem : Name the property or operation used in each of the following steps:

1. 2x < 5 - x
2. 2x + x < 5 - x + x
3. 3x < 5 + 0
4. 3x < 5
5. <
6. 1x <
7. x <

Problem : Name the property or operation used in each of the following steps:

1. -2x≤x + 5
2. -2x - x≤x + 5 - x
3. -3x≤0 + 5
4. -3x≤5
5. ≥
6. 1x≥ -
7. x≥ -