## anonymous one year ago How many solutions does the equation have? 2(2x+5)=4(x+3) A. one solution B. infinite solutions C. no solution

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1. SolomonZelman

2(2x+5)=4(x+3) 4x+10=4x+12

2. SolomonZelman

Is that true for any values of x?

3. anonymous

no solution?

4. SolomonZelman

Yes

5. anonymous

Thank You!

6. SolomonZelman

Yw !

7. anonymous

How many solutions does the equation have? a+5=1/5(5a+25) A. one solution B. infinite solutions C. no solution What about this one i think infinite solutions

8. SolomonZelman

$$\large\color{black}{ a+5=\frac{1}{5}(5a+25)}$$ like this?

9. anonymous

yes

10. SolomonZelman

then you are correct - "infinte solutions" is the right answer.

11. SolomonZelman

Because when you expand the right side, you get: $$\large\color{black}{ a+5=\frac{1}{5}(5a+25)}$$ $$\large\color{black}{ a+5=a+5}$$ and that is true for any value of a.

12. anonymous

Thank you again!

13. SolomonZelman

You welcome, again! :)

14. anonymous

I have 3 more

15. anonymous

if you could check them

16. SolomonZelman

Alright...

17. anonymous

How many solutions does the equation have? 4x + 2(x-3)=8x + 12 A. one solution B. infinite solutions C. no solution

18. SolomonZelman

what did you choose?

19. anonymous

A?

20. SolomonZelman

Yes, correct!

21. anonymous

Thank You!!

22. SolomonZelman

yw

23. anonymous

Which expressions would complete this equation so that it has infinitely many solutions? 8 + 2(8x – 6) = Choose exactly two answers that are correct. A. 2(4x + 7) B. 9x – 10 C. 16x – 4 D. 4(4x – 1)

24. SolomonZelman

25. anonymous

C and D?

26. anonymous

Or A and D?

27. SolomonZelman

8 + 2(8x – 6) = 8 + 16x – 12 = 16x – 4.  same = same  ---->  8 + 2(8x – 6) = 16x - 4  C is right

28. anonymous

So C and D?

29. SolomonZelman

8 + 2(8x – 6) = 8 + 4(4x – 3) = 8 + 4(4x – 1 - 2) = 8 + 4(4x – 1) + (-2)(4) = 8 + 4(4x – 1) -8 = 4(4x – 1) =

30. SolomonZelman

yes, C and D

31. anonymous

Thanks Again!!! I have one more

32. SolomonZelman

k

33. anonymous

What is the best way to classify each equation? Column AColumn B 1. 8x + 24=2(4x+12) 2. 5x + 18-x=2(2x+8) 3. 7(3x-2)=20x-13 4. 3x + 2(x-10)=5(x-4) A. identity B. contradiction C. neither @SolomonZelman

34. SolomonZelman

Can you write the Columns more clearly please?

35. anonymous

dont worry about the columns... Column A is with the long equations and Column B is A. identity B. contradiction C. neither

36. SolomonZelman

Column A Column B 1. 8x + 24=2(4x+12) 2. 5x + 18-x=2(2x+8) 3. 7(3x-2)=20x-13 4. 3x + 2(x-10)=5(x-4) like this?

37. anonymous

what you have underneath column B is suppose to be under Column A and under Column B is suppose to be this A. identity B. contradiction C. neither

38. SolomonZelman

Column A Column B 8x+24=2(4x+12) Identity 5x+18-x=2(2x+8) Contradiction 7(3x-2)=20x-13 Niether 3x+2(x-10)=5(x-4) like this?

39. anonymous

yes

40. SolomonZelman

(When you expand 1st row, 1st column) 8x+24=2(4x+12) $$\longrightarrow$$ 8x+24=8x+24

41. SolomonZelman

(Expand 2nd row, 1st column) 5x+18-x=2(2x+8) $$\longrightarrow$$ 5x+18-x=4x+16 (Subtract x from 5x: 5x-x=4x) 5x+18-x=4x+16 $$\longrightarrow$$ 4x+18=4x+16

42. SolomonZelman

So at this point you should be able to tell me whether A is an *identity* (true for all values of x), a *contradiction* (true for NO values of x - i.e. always false) OR *Niether* (not contradition or identity - i.e. has 1 solution)

43. SolomonZelman

(Expand 3rd row, 1st column) 7(3x-2)=20x-13 $$\longrightarrow$$ 21x-14=20x-13 (Subtract 20x from both sides) 21x-14=20x-13 $$\longrightarrow$$ x-14=13 (Add 14 to both sides) x-14=13 $$\longrightarrow$$ x=27 (and this is Niether)

44. SolomonZelman

(Expand 4th row, 1st column) 3x+2(x-10)=5(x-4) $$\longrightarrow$$ 3x+2x-20=5x-20 (Add like terms on the left side) 3x+2x-20=5x-20 $$\longrightarrow$$ 5x-20=5x-20 Can you identify this one as either: *identity*, *contradiction*, or *Neither*

45. anonymous

sorry I had to leave but im back @SolomonZelman

46. SolomonZelman

47. anonymous

ok

48. anonymous

so 1.A 2.B. 3.C 4.A?

49. SolomonZelman

yes, Identity Contradition Neither Identity *CORRECT!*

50. anonymous

THANK YOU!!!!!!!

51. SolomonZelman

Anytime:)

52. anonymous

I got 100%

53. SolomonZelman

Nice to hear that:)

54. SolomonZelman

have a good night!