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Question 1

A)
Correctly select the order of the steps to solve this equation.
−5x+2=67
(1 point)
Add 5 to both sides of the equation.

Step 1:
Step 2:

Add 67 to both sides of the equation.


Add 2 to both sides of the equation.

Multiply -5 on both sides of the equation.
Divide both sides of the equation by -5.

Subtract 2 from both sides of the equation.

Subtract 5 from both sides of the equation.
B)
Solve for x.
(1 point)
x = −3
5
x=−69
5
x =−13
x =13
−5x+2=67
Question 2
A)
Correctly select the order of the steps to solve this equation.
r
5
(1 point)
Step 1:
Step 2:

−6=−1
Add 5 to both sides of the equation.


Multiply 5 on both sides of the equation.
Add 6 to both sides of the equation.

Subtract 6 from both sides of the equation.

Divide both sides of the equation by 5.
B)
Solve for r.
(1 point)
r = 5
r = 25
r = 35
r = 10
r
5
−6=−1
Question 3
A)
Correctly select the order of the steps to solve this equation.
−8−3x=10
(1 point)

Add 10 to both sides of the equation.


Step 1:
Step 2:

Add 8 to both sides of the equation.

Add 3 to both sides of the equation.

Divide both sides of the equation by 3.
Multiply both sides of the equation by 3.

Divide both sides of the equation by -3.
Subtract 8 from both sides of the equation.
B)
Solve for x.

Subtract 3 from both sides of the equation.
−8−3x=10
(1 point)
x = -54
x = -6
x = 54
x = 6
Question 4
A)
Correctly select the order of the steps to solve this equation.
3(2x−9) = 33
(1 point)

Divide by on both sides of the equation.
3


Step 1:
Step 2:
Step 3:

Multiply by on both sides of the equation.
Subtract 6 from both sides of the equation.
Subtract 9 from both sides of the equation.
3

Add 9 to both sides of the equation.

Divide by 2 on both sides of the equation.

Multiply by 2 on both side of the equation.
B)
Solve for x.
(1 point)
x = -30
x = -20
x = 20
x = 10
3(2x−9) = 33
Question 5
A) In Atlanta, the temperature was
−2 °F
in the morning in the winter. There was a winter
storm, and the temperature dropped 10 degrees. What is the temperature now? (1 point)
−12 °
12 °
F
−8 °
F
F
8 °
F
Question 6
A)
Correctly select the order of the steps to solve this equation.
−5(5x−30) = 50
(1 point)


Step 1:
Step 2:
Step 3:
Multiply both sides of the equation by
−5
Subtract 30 from both sides of the equation.


Divide both sides of the equation by

−5
Multiply both sides of the equation by 5.
Add 30 to both sides of the equation.
B)
Solve for x.

Divide both sides of the equation by
−5(5x−30) = 50
(1 point)
x = 5
x = 20
x = 4
x = -20
5
Question 7
A) Solve the following 1 step Equation:
7
23-23-7
Question 8
A) Solve the following multi-step Equation:
4
2-4-2
Question 9
x - 8 = -15 (1 point)
3 (2y + 6) = 30 (1 point)
A) Solve the following multi-step Equation: -5 (9w + 8) = 50 (1 point)
2-2
9-9
Question 10
A) Solve the following multi-step Equation: -5
5
12.5-12.5
Question 11
6(-2x - 5) = 30 (1 point)
A) Solve the following two-step Equation: 2s - 12 = 20 (1 point)-16
4
16-4
Question 12
A)
Solve the following two-step Equation:
r
4 − 1 = 2
(1 point)
8-12-8
12
Question 13
A) Solve the following two-step Equation:
4-3-4
3
4 = 4j - 8 (1 point)
Question 14
A) Solve the following two-step Equation: 3 + 3t = 12 (1 point)
9-12
12
3
Question 15
A)
Solve the following two-step Equation:
p
3 + 5 = 9
(1 point)
42-42
12-1

5 answers

Let's go through the questions one by one, providing the correct order of steps and solutions.

Question 1:

A) Correct order of steps to solve the equation \( -5x + 2 = 67 \):

  • Step 1: Subtract 2 from both sides of the equation.
  • Step 2: Divide both sides of the equation by -5.

B) Solve for \( x \):

  1. \( -5x + 2 = 67 \)
  2. Subtract 2 from both sides: \( -5x = 65 \)
  3. Divide by -5: \( x = -13 \)

Answer: \( x = -13 \)

Question 2:

A) Correct order of steps to solve the equation \( \frac{r}{5} - 6 = -1 \):

  • Step 1: Add 6 to both sides of the equation.
  • Step 2: Multiply both sides of the equation by 5.

B) Solve for \( r \):

  1. \( \frac{r}{5} - 6 = -1 \)
  2. Add 6 to both sides: \( \frac{r}{5} = 5 \)
  3. Multiply by 5: \( r = 25 \)

Answer: \( r = 25 \)

Question 3:

A) Correct order of steps to solve the equation \( -8 - 3x = 10 \):

  • Step 1: Add 8 to both sides of the equation.
  • Step 2: Divide both sides of the equation by -3.

B) Solve for \( x \):

  1. \( -8 - 3x = 10 \)
  2. Add 8: \( -3x = 18 \)
  3. Divide by -3: \( x = -6 \)

Answer: \( x = -6 \)

Question 4:

A) Correct order of steps to solve the equation \( 3(2x - 9) = 33 \):

  • Step 1: Divide by 3 on both sides of the equation.
  • Step 2: Add 9 to both sides of the equation.
  • Step 3: Divide by 2 on both sides of the equation.

B) Solve for \( x \):

  1. \( 3(2x - 9) = 33 \)
  2. Divide by 3: \( 2x - 9 = 11 \)
  3. Add 9: \( 2x = 20 \)
  4. Divide by 2: \( x = 10 \)

Answer: \( x = 10 \)

Question 5:

What is the temperature after dropping 10 degrees from \( -2 °F \)?

  1. \( -2 - 10 = -12 °F \)

Answer: \( -12 °F \)

Question 6:

A) Correct order of steps to solve the equation \( -5(5x - 30) = 50 \):

  • Step 1: Divide both sides of the equation by -5.
  • Step 2: Add 30 to both sides of the equation.
  • Step 3: Divide by 5.

B) Solve for \( x \):

  1. \( -5(5x - 30) = 50 \)
  2. Divide by -5: \( 5x - 30 = -10 \)
  3. Add 30: \( 5x = 20 \)
  4. Divide by 5: \( x = 4 \)

Answer: \( x = 4 \)

Question 7: Solve \( 23 - 23 - 7 \):

  1. \( 23 - 23 = 0 \)
  2. \( 0 - 7 = -7 \)

Answer: \( -7 \)

Question 8: Solve \( 2 - 4 - 2 \):

  1. \( 2 - 4 = -2 \)
  2. \( -2 - 2 = -4 \)

Answer: \( -4 \)

Question 9: Solve \( x - 8 = -15 \):

  1. Add 8: \( x = -15 + 8 \)
  2. \( x = -7 \)

Solve \( 3(2y + 6) = 30 \):

  1. \( 3 \cdot 2y + 18 = 30 \)
  2. \( 6y + 18 = 30 \)
  3. \( 6y = 12 \)
  4. \( y = 2 \)

Solve \( -5(9w + 8) = 50 \):

  1. \( -45w - 40 = 50 \)
  2. Add 40: \( -45w = 90 \)
  3. \( w = -2 \)

Question 10: Solve \( 12.5 - 12.5 \): Answer: \( 0 \)

Question 11: Solve \( 6(-2x - 5) = 30 \):

  1. \( -12x - 30 = 30 \)
  2. Add 30: \( -12x = 60 \)
  3. \( x = -5 \)

Solve \( 2s - 12 = 20 \):

  1. Add 12: \( 2s = 32 \)
  2. \( s = 16 \)

Question 12: Solve \( \frac{r}{4} - 1 = 2 \):

  1. Add 1: \( \frac{r}{4} = 3 \)
  2. Multiply by 4: \( r = 12 \)

Question 13: Solve \( 4 - 4 = 4j - 8 \):

  1. \( 0 = 4j - 8 \)
  2. Add 8: \( 8 = 4j \)
  3. \( j = 2 \)

Question 14: Solve \( 3 + 3t = 12 \):

  1. Subtract 3: \( 3t = 9 \)
  2. \( t = 3 \)

Question 15: Solve \( \frac{p}{3} + 5 = 9 \):

  1. Subtract 5: \( \frac{p}{3} = 4 \)
  2. Multiply by 3: \( p = 12 \)

If you have further questions or need clarifications on any specific question, feel free to ask!

Solve the following multi-step Equation: 6(-2x - 5) = 30

To solve the equation \( 6(-2x - 5) = 30 \), follow these steps:

  1. Distribute the 6: \[ 6 \cdot -2x + 6 \cdot -5 = 30 \ -12x - 30 = 30 \]

  2. Add 30 to both sides: \[ -12x - 30 + 30 = 30 + 30 \ -12x = 60 \]

  3. Divide both sides by -12: \[ x = \frac{60}{-12} \ x = -5 \]

Thus, the solution to the equation \( 6(-2x - 5) = 30 \) is: \[ \boxed{-5} \]

Solve the following two-step Equation: 4 = 4j - 8

To solve the equation \( 4 = 4j - 8 \), follow these steps:

  1. Add 8 to both sides to isolate the term with \( j \) on one side: \[ 4 + 8 = 4j - 8 + 8 \ 12 = 4j \]

  2. Divide both sides by 4 to solve for \( j \): \[ j = \frac{12}{4} \ j = 3 \]

Thus, the solution to the equation \( 4 = 4j - 8 \) is: \[ \boxed{3} \]

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