Question

Samuel is solving the equation 3(x - 1) + 4 = 2 - (x + 3). Which equivalent equations might Samuel use? Select the TWO correct answers.

a
3x - 3 + 4 = 2 - x - 3
b
3x + 1 = -x - 1
c
3x + 3 = -x + 5
d
3x - 1 + 4 = 2 - x + 3
e
3x - 3 + 4 = 2 - x + 3
f
3x + 1 = -x + 5

Answer 1

Answer:C

D

Explanation:

Answer 2

A= 3, and 4. (c & d)

1. Solve the Equation:
`3(x - 1) + 4 = 2 - (x + 3)\\`, to get

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1a. Use the distributive property to multiply 3 by x−1.

`3x−3+4=2−(x+3)`

1b. Add −3 and 4 to get 1.

`3x+1=2−(x+3)`

1c. To find the opposite of x+3, find the opposite of each term.

`3x+1=2−x−3`

1d. Subtract 3 from 2 to get −1.

`3x+1=−1−x`

1e. Add x to both sides.

`3x+1+x=−1`

1f. Combine 3x and x to get 4x.

`4x+1=−1`

1g. Subtract 1 from both sides.

`4x=−1−1`

1h. Subtract 1 from −1 to get −2.

`4x=−2`

1i. Divide both sides by 4.

`x=4−2​`

1j. Reduce the fraction 4−2​=−0.5 to lowest terms by extracting and canceling out 2.

`x=−21​` or x = -21

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Now that you know the answers, solve the others:

2. A= 1, so this is wrong. How I solved it is shown below:

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1a. Add −3 and 4 to get 1.

3x+1=2−x+3

1b. Add 2 and 3 to get 5.

3x+1=5−x

1c. Add x to both sides.

3x+1+x=5

1d. Combine 3x and x to get 4x.

4x+1=5

1e. Subtract 1 from both sides.

4x=5−1

1f. Subtract 1 from 5 to get 4.

4x=4

1g.Divide both sides by 4.

x=44​

1h. Divide 4 by 4 to get 1.

x=1

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3. A= .5, so it is Correct. Work below

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3a. Add x to both sides.

`3x+3+x=5`

3b. Combine 3x and x to get 4x.

`4x+3=5`

3c. Subtract 3 from both sides.

`4x=5−3`

3d. Subtract 3 from 5 to get 2.

`4x=2`

3e. Divide both sides by 4.

`x=42​`

3f. Reduce the fraction 42​=0.5 to lowest terms by extracting and canceling out 2.

`x=21​` (A = 1/2 or .5)

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4. A= .5, so it is correct. Work below. Now we have our 2, so we don't need to do it again.

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4a. Add −1 and 4 to get 3.

`3x+3=2−x+3`

4b. Add 2 and 3 to get 5.

`3x+3=5−x`

4c. Add x to both sides.

`3x+3+x=5`

4d. Combine 3x and x to get 4x.

`4x+3=5`

4e. Subtract 3 from both sides.

`4x=5−3`

4f. Subtract 3 from 5 to get 2.

`4x=2`

4g. Divide both sides by 4.

`x=(2)/(4)`

4h. Reduce the fraction 42​=0.5 to lowest terms by extracting and canceling out 2.

`x=(1)/(2)`