Question

Given: x – (5 – 3x + 2) = 15 + 3x

Prove: x = 22

x – (5 – 3x + 2) = 15 + 3x
Given
x – (5 + 2– 3x) = 15 + 3x

x – (7– 3x) = 15 + 3x

x – 7 + 3x = 15 + 3x

x + 3x – 7 = 15 + 3x
Commutative Property of Addition
4x – 7 = 15 + 3x
Combine Like Terms
x – 7 = 15
Subtraction Property of Equality
x = 22
Addition Property of Equality

Answer 1

What are the missing justification steps, in order?

A. Commutative Property of Addition, Combine Like Terms, Distributive Property

B. Associative Property of Addition, Distributive Property, Multiplication Property of Equality

C. Associative Property of Addition, Commutative Property of Addition, Distributive Property

D. Associative Property of Addition, Distributive Property, Addition Property of Equality

Answer 2

@jim_thompson5910 a? maybe?

Answer 3

perhaps it's wise to point \(\textbf{*where*}\) the missing steps are?

Answer 4

what?

Answer 5

where are the missing steps? there are like a lot of unnamed steps there...where are you supposed to start?

Answer 6

you are correct, the answer is indeed choice A

Answer 7

okay thanks again, I always feel like I'm getting these wrong. too many words..hehe

Answer 8

you're doing fine, just take it one step at a time

Answer 9

Given: 4(x + 1) = 10x – 8
Prove: x = 2 Step

Mathematical Statement

Justification

STEP 0:

4(x + 1) = 10x – 8

Given

STEP 1:

4x + 4 = 10x – 8

Distributive Property

STEP 2:

4 = 6x – 8

Subtraction Property of Equality

STEP 3:

12 = 6x

Addition Property of Equality

STEP 4:

6x = 12

Symmetric Property of Equality

STEP 5:

x = 2

Associative Property of Multiplication

Answer 10

Which step of justification is incorrect, and what should the justification for that step be to solve the equation?

Step 5; Division Property of Equality

Step 1; Commutative Property of Addition

Step 3; Subtraction Property of Equality

Step 2; Addition Property of Equality

Answer 11

C? :o

Answer 12

no, step 3 is just fine...so the answer isn't C

Answer 13

oh :( step 2 ?

Answer 14

step 2 is just fine as well

Answer 15

because in that step, we're subtracting 4x from both sides, which is perfectly valid

Answer 16

take a look at step 5 and look up the definition of the Associative Property of Multiplication

Answer 17

ohhhh its when 3 or more numbers are multiplied!

Answer 18

yes, but we're dividing both sides by 6 to isolate x...so we're actually using the Division Property of Equality

Answer 19

So step 5 is correct, but the reason/justification is incorrect

Answer 20

Okay I got it :) I swear i should start paying you....Lol!

Answer 21

lol it's fine, although I do appreciate the thought

Answer 22

but I'm glad you're understanding it now

Answer 23

haha okay :) & me tooo! I think i got the last two..

Answer 24

alright great

Answer 25

Wait last one I swear. i just wanna check my answer :))

Answer 26

Given: 3x + 1 = 2 + 2x – 4

Prove: x = –3

Given the equation 3x + 1 = 2 + 2x – 4, use the commutative property to rearrange the terms so that like terms are next to one another. This gives the equation 3x + 1 = 2 – 4 + 2x. Then use the associative property of addition to group the like terms. This gives the equation 3x + 1 = (2 – 4) + 2x. Next, combine like terms to get the equation 3x + 1 = – 2 + 2x. Use the subtraction property of equality to subtract 2x from both sides of the equation. This gives the equation x + 1 = – 2. Then use the _________________________ to subtract 1 from both sides of the equation. This gives the solution x = –3. Therefore, given the equation 3x + 1 = 2 + 2x – 4, x is equal to –3.

Which justification was left out of the paragraph proof above?

Answer 27

Subtraction property of equality??

Answer 28

You are correct. The subtraction property of equality allows you to subtract terms from both sides.

Answer 29

yay, thanks. &good night! :)

Answer 30

you're welcome, good night