Question

Drag a statement or reason to each box to complete this proof.

If −3(x+8)=−21, then x=−1.

Statement Reason
1. _________ Given
2. −3(x+8)−/3=−21−3 ____________
3. _________ Simplifying
4. x+8−8=7−8 ______________
5. x=−1 Simplifying

Subtraction Property of Equality
Distributive Property of Equality
Division Property of Equality
x + 8 = 7
-3(x + 8) = -21

Answer 1

@Vocaloid

Answer 2

well we naturally start w/ -3(x + 8) = -21 as "given" because it's given

not sure what's going on w/ step 2 can you check to see if it's written correctly

Answer 3

awesome

any ideas? notice how they are ~dividing~ by -3 on each side

Answer 4

2nd is division

Answer 5

good, the Division Property of Equality

now the third step is "simplifying" so which answer choice do you get if you take

-3(x + 8)/(-3) and simplify? notice how the -3 cancels out

Answer 6

x + 8 = 7

Answer 7

awesome so that's blank 3

for blank 4 notice how we are ~subtracting~ 8 from each side so which property would this be?

Answer 8

subtraction property of equality

Answer 9

awesome

so in order

blank 1 = -3(x + 8) = -21
blank 2 = Division Property of Equality
blank 3 = x + 8 = 7
blank 4 = Subtraction Property of Equality

Answer 10

is this correct

Answer 11

good

Answer 12

may I see what steps 1-3 are? they weren't included in the screengrabs you posted

Answer 13

hold on i'm sorry

Answer 14

well, statement 1 just re-states what is already given so "given" would be the appropriate choice

step 2 goes from 3(x-4) to 3x - 12, which property is this?

Answer 15

distributive property

Answer 16

good

step 3 adds 12 to both sides, which property is this?

Answer 17

addition property

Answer 18

awesome

so step 4 is simplifying

3x - 12 + 12 = x + 4 + 12

which answer choice do you get after you take that expression + combine like terms?

Answer 19

3x = x + 16

Answer 20

good

Answer 21

for step 5 they subtract x from each side, which property is this?

Answer 22

subtraction property

Answer 23

good, and step 6 is simplifying so what do you get when you combine like terms for

3x - x = x + 16 - x?

Answer 24

2x = 16

Answer 25

awesome

so step 7 divides both sides by 2, which property is this?

Answer 26

division property of equality

Answer 27

good

last step, step 8

what is the result when you simplify 2x/2 = 16/2 ?

Answer 28

x = 8

Answer 29

awesome

so to re-cap

step 1: given
2: distributive
3: subtraction
4: 3x = x + 16
5: subtraction
6. 2x = 16
7; division
8: x = 8

Answer 30

wait

Answer 31

step 3 is addition sorry

Answer 32

yea cause i just started wondering

Answer 33

Which property justifies this statement?

If 4x = 20, then x = 5.


A. Substitution Property of Equality

B. Subtraction Property of Equality

C. Reflexive Property of Equality

D. Division Property of Equality

Answer 34

any ideas? did they add, multiply, subtract, or divide?

Answer 35

IT'S D

Answer 36

Which property justifies this statement?

x − 4 = x − 4


A. Substitution Property of Equality

B. Reflexive Property of Equality

C. Transitive Property of Equality

D. Symmetric Property of Equality

Answer 37

I BELIEVE IS B

Answer 38

good

Answer 39

are they both correct ?

Answer 40

yes

Answer 41

i'll start a new question if that's ok

Answer 42

sure