# Like Inequalities Can Be Added

If x < y and w < z, then x + w < y + z |

Example

If 2 < x < 5 and 3 < y < 5, which one of the following best describes x â€“ y?

- â€“3 < x â€“ y < 2
- â€“3 < x â€“ y < 5
- 0 < x â€“ y < 2
- 3 < x â€“ y < 5
- 2 <
*x*â€“*y*< 5

Solution

Multiplying both sides of 3 <
Now, we usually write the smaller number on the left side of the inequality. So â€“3 > â€“
Add this inequality to the like inequality 2 <

*y*< 5 by â€“1 yields â€“3 > â€“*y*> â€“5.*y*> â€“5 becomes â€“5 < â€“*y*< â€“3.*x*< 5:The answer is (A).