9th grade math help!!!?

Question

Here's the question, can you please help me? Thanks!!!

In transforming algebraic expressions to equivalent forms, it's easy to make some mistakes and use "illegal" moves. Given below are 6 pairs of algebraic expressions. Some are equivalent and some are not.
- Use tables, graphs, and/ or algebraic reasoning to decide which pairs are actually equivalent and which involve errors in reasoning.
- In each case of equivalent expressions, describe algebraic reasoning that could be used to show equivalence.
-In each case of an algebra mistake, spot the error in reasoning. Write an explanation that would help clear up the problem for a student who made the error.

A. Is 3(2x+8) equivalent to 6x+8?
B. Is 4x-6x equivalent to 2x?
C. Is 8(2-6x) equivalent to 16-48x?
D. Is 10 + 3x- 12 equivalent to 3x+12?
E. Is 5x+ 10 over 5, equivalent to x + 10?
F. Is -4(x-3) equivalent to -4x-12 ?

No rude comments like " Do your own math" or something, please. i just finished doing A LOT, and don't feel like doing more, also i'm terrible at math:/

And again, thank you so much if you answer!!

Answer 1

A. You have to distribute the 2 into the 8 as well making it 6x+24

B. There is a (-) before the 6x so the answer is actually (-)2

C. Equivalent because it distributes both numbers in the parentheses.\

D. You have to combine like terms and due to keep, change, change 3x - 12 is actually 3x + -12. So combine 10 + -12 to make -2. Therefore the answer is 3x -2

E. You have divide the 5 from both the 5x and the 10. So 5x/5 = 5 and 10/5 = 2 so the answer really is x + 2

F. Its a negative times a negative when it comes to the second number in the parentheses so the answer should be positive. So the answer should really be -4x + 12

Answer 2

Starting with A: the rules of algebra say we can expand 3(2x+8) out by multiplying what is in the brackets by 3, then we have 6x+24, this is clearly not equivalent to 6x+8

B. 4x-6x, again we can use "normal rules" to subtract, so we have x(4-6) (factorising out x) so this gives us -2x which is not equivalent

C. Using the same reasoning as A we have 16-48x which is the answer so therefore equivalent

D. 3x-12+10 is the same as 3x-2 (we just add the -12 and 10 as normal) so this is not equivalent

E. 5x+10 all over 5 means we divide by 5 so we have 5x/5+10/5 which is x+2 so this is not equivalent

F. we multiply out in the usual way taking care with negative signs, and we get -4x+12 which is not equivalent to the answer given.



How a student can avoid these mistakes

A. Multiplying everything in the bracket by 3

B. taking care with negatives, -6+4 is different to 4-6

C. answer is correct

D. Making sure again to add/subtract correctly

E. Making sure to divide every part of the numerator (top of the fraction) by the denominator (the bottom of the fraction, in this case 5)

F. being careful with negatives, so -4*-3=+12 ( as two negatives multiplied gives a positive)



I hope this helps

Answer 3

A.Not equivalent because 3(2x+8)=6x+24. Seperate the 2x and 8 if it's helpful to make it clear you need to multiply both 2x and 8.

B. Not equivalent b/c 4x-6x=-2x. remember to check if the answer is negative or positive.

C.Yes, it's equivalent b/c 8x2=16 and 8x6=48.

D. No. 10+3x-12=3x-2. seperate the 3x and 10-12 if that helps.

E. No. 5x+10 over 5 is x+2. Remember to reduce BOTH numbers.

F. No. -4(x-3)=-4x+12. Remember double negatives equals positive.



Hope this helps!

Answer 4

A.no 3(2x+8) is 6x+24

B. yes

C. yes

D. no 10+3x-12=3x-2

E. no 5x+10 over 5 is x+2

F. yes

Answer 5

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