## anonymous one year ago What values of x make the two expressions below equal? (2x+1)(x-7)/11(x-7)= 2x+1/11 A. All real numbers B. All real numbers except -1/2 C. All real numbers except 7 D. All real numbers except -1/2 and 7

1. DanJS

missing parenthesis

2. DanJS

maybe

3. anonymous

The best way to go about this problem is for you to plug in the numbers where stated "except"" to see if they work.

4. DanJS

$\frac{ (2x+1)(x-7) }{ 11(x-7) }=\frac{ 2x+1 }{ 11 }$ is that it

5. anonymous

yes that's what I wrote

6. anonymous

If not A, but if they do you'd be picking one of the B to D. Simple right?

7. DanJS

group the entire numerator in a bra kets

8. DanJS

simplify, (x-7) can cancel in the first, but you must keep in mind that x cant be 7, it will make the original expression undefined

9. DanJS

then both are over 11, and you can multiply both sides by 11 to cancel those... left with 2x+1 = 2x+1 , true, all reals

10. anonymous

so if you cancel x-7 out, top and bottom you're left with (2x+1)-11 right?

11. anonymous

/11

12. DanJS

yes, $\frac{ 2x+1 }{ 11 }= \frac{ 2x+1 }{ 11 }$

13. DanJS

It is like saying, 1 = 1, True statement, any value for x is possible there

14. DanJS

remember you canceled out (x-7) in the denominator though, so x-7 can not be zero

15. anonymous

same exact thing on both sides except the left one has parentheses

16. DanJS

right, if you have the same things on both sides, then the variable can be any real number. Except here it can not be 7 since you cancelled out x-7 in the denominator, you cant have x-7=0 or x=7

17. DanJS

zero in the bottom is bad

18. anonymous

so it would be all real numbers except 7?

19. DanJS

yes

20. anonymous

thank you ;)-

21. anonymous

:)

22. DanJS

i forget what they call those solutions x=7, some term

23. anonymous

did not know that myself haha

24. DanJS

you can check, put x=7 and see if both sides are the same...

25. anonymous

i did

26. DanJS

extraneous solutions, just popped into my head, check that definition out if it sounds familiar.