Question

The steps in the simplification of the expression 9 + 3x + 2y − 2x – y − 8 are shown below.

Step 1: 9 – 8 + 3x − 2x + 2y − y
Step 2: (9 − 8) + (3x − 2x) + (2y − y)
Step 3: 1 + x (3 − 2) + y (2 − 1)
Step 4: 1 + x (1) + y (1)
Step 5: 1 + x + y

Which statement is correct?

Answer 1

Step 2 uses associative property of addition, and step 4 uses the multiplicative identity.

Step 2 uses associative property of multiplication, and step 3 uses commutative property of addition.

Step 1 uses distributive property of addition, and step 5 uses distributive property of multiplication.

Step 1 uses commutative property of addition, and step 2 uses simplification.

Answer 2

From equation (4) to equation (5) uses the multiplicative identity. Which step is that?
http://www.icoachmath.com/math_dictionary/Multiplicative_Identity.html

Answer 3

Well I'm not exactly sure. I was thinking the answer would be the last option Step 1 uses commutative property of addition, and step 2 uses simplification

Answer 4

Equation (1) to equation (2) uses associative property of addition. What step is that?

Answer 5

I know the defs, I'm confused about the relation between the equations given and the "steps"

Answer 6

Being able to group things in a different way ( and show order of operations with parentheses) is associative.

Answer 7

Oh ok! So would it be the first option then?

Answer 8

I think step 1 is the operation that produces the equation you list next to step 1. OK?

Answer 9

Are you not sure what it is then..? Because i'm sorta confused :/

Answer 10

So step 1 is kind of associative but without the parentheses, and step 2 is the actual parentheses and so the actual associative step. In any case options 3 and 4 seem incorrect.

Answer 11

A step has to be the operations that transform one equation into the next. It's a relationship between two equations. You list steps as if they were equations. That's what was confusing.

Answer 12

So it's between A or B you're saying?

Answer 13

I think it's the first option then

Answer 14

I think so, but I don't like either one of those either.
If step 4 is the operation that produces the equation shown next to (5), that's the multiplicative identity. Step 4 is just subtraction.

Answer 15

Sorry, next to (4)

Answer 16

Say it again:

Step 4: 1 + x (1) + y (1)
Step 5: 1 + x + y

The operation to go from the first to the second is the multiplicative identity.
According to the rules of this game, I think this should be step 5.

Answer 17

Step 1: 9 – 8 + 3x − 2x + 2y − y
Step 2: (9 − 8) + (3x − 2x) + (2y − y)

The operation to go between these two is the associative property.

Answer 18

wouldn't it just be simplification though?

Answer 19

Simplification is not a fundamental operation. It makes uses of them.

Answer 20

Ok. But, if I had to put an answer write now, I would think the first option is the one that makes the most sense

Answer 21

Step 2: (9 − 8) + (3x − 2x) + (2y − y)
Step 3: 1 + x (3 − 2) + y (2 − 1)

The operation to go between these two is the distributive property of multiplication.

Answer 22

OK, but I don't like it. Multiplicative identity should be step 5.

Answer 23

Ok what do you think seems best?

Answer 24

I think the question is in error and they probably mean for you to pick answer you liked (#1).

Answer 25

Ok well I guess i will put that option. Thank you so much! You're a lifesaver!

Answer 26

Cross my fingers.