SOLUTION: My book didn't show me how to do this but it asks questions like this anyway. The length of any side of a triangle is less than the sum of the lengths of the other two sides. In

Question 1063823: My book didn't show me how to do this but it asks questions like this anyway.
The length of any side of a triangle is less than the sum of the lengths of the other two sides. In triangle[PQR], PR= RQ+4 and RQ<11. Write and solve an inequality for PQ.
Any explanations of steps would be great.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
For a given triangle PQR, the sum of any two sides is greater than the third and any side is less than the sum of the other two
:
1) PQ + PR > RQ
:
2) PQ + RQ > PR
:
3) RQ + PR > PQ
:
4) RQ < 11
:
5) PR = RQ + 4
:
by inequality 2) and equation 5)
:
PQ + RQ > RQ + 4
:
6) PQ > 4
:
any side of PQR is less than the sum of the other two sides, also use inequality 4)
:
RQ < PQ + PR < 11
:
use equation 5)
:
RQ < PQ + RQ + 4 < 11
:
7) 0 < PQ < 7
:
******************************
combine inequalities 6) and 7)
:
4 < PQ < 7
*****************************
:
RELATED QUESTIONS
Could someone please help with this problem? It is a question on my homework assignment... (answered by scott8148)

i'm doing a SAT practice test and i found a very simple question that I thought the... (answered by richwmiller)

i'm doing a SAT practice test and i found a very simple question that I thought the... (answered by richwmiller,LinnW)

Can you please show me how to figure this out: Les Hinckle made a deposit in the bank on (answered by stanbon)

PQ, PR and QR are tangents to a circle at point S, U and T respectively. Given that... (answered by Fombitz,Alan3354)

PLEASE help me with this.... one side of a triangle has a length of 5x-2. a longer side... (answered by bucky)

Okay, so I need help fully understanding how the Pythagorean theorem works in a question... (answered by ankor@dixie-net.com,stanbon)

This is a unusual question but I came here because I don’t have anyone else to ask... (answered by MathLover1,ikleyn)

Hello, I have a question that I am having a lot of trouble with. I'll give you the... (answered by solver91311)