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

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

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

------------------------------------------

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

-------------------------------------

Now that you know the answers, solve the others:

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

-----------------------------------

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

----------------------------

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

-----------------------------

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)

-----------------------------

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

-------------------------------

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.

$x=\frac{2}{4}$

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

$x=\frac{1}{2}$