Help on #1 a b c I really need help and I hope you guys help me get a better understanding

Algebra
Tutor: None Selected Time limit: 1 Day

Aug 14th, 2015

Thank you for the opportunity to help you with your question!

Since A is between B and C then clearly we can see that the distance BC would be equal to the distance BA plus the distance AC. So we would have the following expression:

BC = BA + AC

So the problem says:   AB = 4x - 3  ;    BC = 7x + 5   ;    AC = 5x - 16

Then we need to enter 4x - 3 in place of AB, 7x + 5 in place of BC, and 5x - 16 in place of AC into the above equation. So we would have the following:

BC = BA + AC  --------------->   7x + 5 = 4x - 3 + 5x - 16

So we need to solve the above equation for x like this.

7x + 5 = 4x - 3 + 5x - 16  ---------------> 7x + 5 = 4x + 5x - 3 - 16   ----------------->  7x + 5 = 9x - 19

7x + 5 = 9x - 19  ------------------>  7x - 7x + 5 = 9x - 7x - 19  ---------------------> 0 + 5 = 2x - 19

5 = 2x - 19  -------------------->  5 + 19 = 2x - 19 + 19  ----------------------> 24 = 2x + 0  ------------> 24 = 2x

24 = 2x  --------------------> 24/2 = 2x/2  -----------------------> 12 = x  ------------------->   x = 12

Finally, we enter the obtained x value (x = 12) into the equations of AB, BC, and AC. So we have:

AB = 4x - 3  ---------------->  AB = 4(12) - 3  -----------------> AB = 48 - 3  ------------------>  AB = 45

BC = 7x + 5 ---------------->  BC = 7(12) + 5 -----------------> BC = 84 + 5 ----------------->  BC = 89

AC = 5x - 16 ----------------> AC = 5(12) - 16 -----------------> AC = 60 - 16 ----------------> AC = 44

Final answer:  AB = 45 ; BC = 89 ; AC = 44

Please let me know if you need any clarification. I'm always happy to answer your questions.
Aug 14th, 2015

Omg thank you so much would you also mind helping me with the others please 

Aug 14th, 2015

I've done two can you help with the others

Aug 14th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Aug 14th, 2015
...
Aug 14th, 2015
Dec 2nd, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer