PLEASE EXPLAIN WILL GIVE BRAINLIEST What is the smallest integer x, for which x, x+5, and 2x−15 can be the lengths of the sides of a triangle?

11

Step-by-step explanation:

Interesting question. Thanks for posting.

The key to the answer is in 2x - 15

If x = anything less than 7.5 (which is not an integer) then 2x - 15 will be minus and minus lengths in geometry cannot be. Not at this level anyway.

So, the smallest integer that x could be would be 8.

That would make 2x - 15 = 1

We're not quite finished. We have to check that out.

x = 8

x + 5 = 13

2x - 15 = 1

It doesn't work. 1 and 8 don't make more than 13.

Try again.

Let's see.  Let's try 10

2*10 - 15 = 5.

x + 5 = 15

x = 10

This doesn't work either, because 10 and 5 = 15 which won't make a triangle. The two smallest sides of a triangle have to be more than the largest side. But notice how close we are. Let's try 11.

2*11 - 15 = 7

x + 5 = 16

x = 11

and this works. 11 + 7 = 18 which is more than 16.

1. 8

2. 9

3. 20

4. 3

5. 17

6. 2.2

7. 11.25

8. 1

9. 14

10. 2

step-by-step explanation:

thats the first half