1 of 81 of 8 Items

Question

Question 1
Consider this equation:

4(3x−2)=−24


Correctly order the steps used to solve this equation.

(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Step 1:
Step 2:
Step 3:
Question 2
Consider this equation:

4(3x−2)=−24

Determine the value of x.

(1 point)
Responses

x=−6
x is equal to negative 6

x=−4
x is equal to negative 4

x=−43
x is equal to negative 4 thirds

x=83
x is equal to 8 thirds
Skip to navigation

page 18 of 18

Answer 1

To solve the equation \( 4(3x - 2) = -24 \), let's go through the steps and then determine the value of \( x \).

Step-by-step solution:

1. Step 1: Distribute the 4 on the left side of the equation:
   \[ 4(3x) - 4(2) = -24 \]
   Which simplifies to:
   \[ 12x - 8 = -24 \]

2. Step 2: Add 8 to both sides to isolate the term with \( x \):
   \[ 12x - 8 + 8 = -24 + 8 \]
   Which simplifies to:
   \[ 12x = -16 \]

3. Step 3: Divide both sides by 12 to solve for \( x \):
   \[ x = \frac{-16}{12} \]
   Which simplifies to:
   \[ x = \frac{-4}{3} \]
   Or in decimal form:
   \[ x = -\frac{4}{3} \]

Final answer for the value of \( x \):

• \( x = -\frac{4}{3} \) (or "x is equal to negative 4 thirds").

Summary of the answers to fill in your form:

• Step 1: Distribute the 4: \( 12x - 8 = -24 \).
• Step 2: Add 8 to both sides: \( 12x = -16 \).
• Step 3: Divide by 12: \( x = -\frac{4}{3} \).

From the available responses for Question 2, the correct answer is:

• \( x = \frac{-4}{3} \) or "x is equal to negative 4 thirds."

Answer 2

Consider this equation:

4(3x−2)=−24


Correctly order the steps used to solve this equation.

(1 point)
Subtract 2 from both sides of the equation.
Divide both sides of the equation by 4 .
Add 2 to both sides of the equation.
Multiply both sides of the equation by 4.
Divide both sides of the equation by 3 .
Multiply both sides of the equation by 3 .

Answer 3

To solve the equation \( 4(3x - 2) = -24 \), let's identify the correct order of the steps and discard those that are unnecessary based on the equation.

Here’s the clear order of operations:

1. Multiply both sides of the equation by \(\frac{1}{4}\) or divide both sides by 4.
   This gives us:
   \[ 3x - 2 = -6 \]

2. Add 2 to both sides of the equation.
   This gives us:
   \[ 3x = -4 \]

3. Divide both sides of the equation by 3.
   This gives us:
   \[ x = -\frac{4}{3} \]

So, the correct ordering of the steps is:

1. Divide both sides of the equation by 4.
2. Add 2 to both sides of the equation.
3. Divide both sides of the equation by 3.

Feel free to replace the steps if they don't directly correspond to the options provided. If you need to discard any unnecessary options like "Subtract 2" or "Multiply both sides by 3," you can focus on the necessary operations above.

Answer 4

2 of 82 of 8 Items

Add 4 to both sides of the equation.
Subtract 4 from both sides of the equation.
Multiply both sides of the equation with -2.
Divide both side of the equation by -2 .
Subtract 2 from both sides of the equation.
The equation has been solved. There are no more steps.

Question 1
Consider this equation:

−2(4+n)=24

Correctly order the steps used to solve this equation.

(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Step 1:
Step 2:
Step 3:
Question 2
Solve for n.

−2(4+n)=24


(1 point)
Responses

n = 16
n = 16

n = -8
n = -8

n = 8
n = 8

n = -16
n = -16
Skip to navigation

page 18 of 18

Answer 5

To solve the equation \( -2(4+n) = 24 \), let's determine the correct sequence of steps and then find the value of \( n \).

Step-by-step solution:

1. Step 1: Divide both sides of the equation by \(-2\).
   \[ \frac{-2(4+n)}{-2} = \frac{24}{-2} \] This simplifies to:
   \[ 4+n = -12 \]

2. Step 2: Subtract 4 from both sides of the equation.
   \[ n = -12 - 4 \]
   This simplifies to:
   \[ n = -16 \]

3. Step 3: The equation has been solved. There are no more steps.

Summary of the correct order of steps:

• Step 1: Divide both sides of the equation by -2.
• Step 2: Subtract 4 from both sides of the equation.
• Step 3: The equation has been solved. There are no more steps.

Final answer for Question 2:

• The value of \( n \) is:
  • \( n = -16 \)

You can fill in the steps and the answer accordingly!

Answer 6

3 of 83 of 8 Items

Question 1
Consider this equation.

58(x+12)=100


Correctly order the steps used to solve this equation.
5/8 (x + 1/2) = 100
(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Divide both sides of the equation by (8)/(5)
Subtract (1)/(2) from both sides of the equations.
Multiply both sides of the equation by (8)/(5)
Add (1)/(2) to both sides of the equations.
Step 1:
Step 2:
Question 2
Solve for x.

5/8(x + 12)=100

(1 point)
Responses

160 1/2
160 and 1 half

62
62

159 1/2
159 and 1 half

63
63
Skip to navigation

page 18 of 18

Answer 7

To solve the equation \( \frac{5}{8}(x + 12) = 100 \), let's determine the correct sequence of steps and subsequently find the value of \( x \).

Step-by-step solution:

1. Step 1: Multiply both sides of the equation by \( \frac{8}{5} \): \[ \left(\frac{8}{5}\right) \cdot \frac{5}{8}(x + 12) = 100 \cdot \frac{8}{5} \] This simplifies to: \[ x + 12 = 160 \]

2. Step 2: Subtract \( 12 \) from both sides of the equation: \[ x = 160 - 12 \] This further simplifies to: \[ x = 148 \]

Correct order of steps:

• Step 1: Multiply both sides of the equation by \( \frac{8}{5} \).
• Step 2: Subtract \( 12 \) from both sides of the equation.

Final answer for Question 2:

• The value of \( x \) is \( 148 \).

Provided Options:

It seems the provided options only account for specific values, and none of my calculations yielded those results. If you mean the equation started as \( \frac{5}{8}(x + 12) = 100 \) just as you stated but have a different value, let's calculate that again:

• The correct steps involve multiplying both sides by \((8/5)\), then subtracting 12.
• The final step reveals \(x = 148\).

Make sure the equation you're referring to was entered correctly, as with these steps, the output does not align with the provided options.

Answer 8

Solve for x.

5/8 (x + 1/2 ) = 100

Answer 9

To solve the equation

\[ \frac{5}{8} \left( x + \frac{1}{2} \right) = 100, \]

we can follow these steps:

Step 1: Multiply both sides by the reciprocal of \(\frac{5}{8}\)

Multiply both sides by \(\frac{8}{5}\):

\[ \frac{8}{5} \cdot \frac{5}{8} \left( x + \frac{1}{2} \right) = 100 \cdot \frac{8}{5}. \]

This simplifies to:

\[ x + \frac{1}{2} = 160. \]

Step 2: Subtract \(\frac{1}{2}\) from both sides

To isolate \(x\), subtract \(\frac{1}{2}\):

\[ x = 160 - \frac{1}{2}. \]

This can also be expressed in fractions or decimals:

\[ x = 160 - 0.5 = 159.5. \]

Final Answer

So, the solution for \(x\) is

\[ x = 159.5 \quad \text{or} \quad x = 159 \frac{1}{2}. \]

Answer 10

4 of 84 of 8 Items

Add 10 to both sides of the equation.
Multiply both sides of the equation by -30 .
Divide both sides of the equation by -30 .
Subtract 10 from both sides of the equation.
Add 300 to both sides of the equation.
Subtract 300 from both sides of the equation.

Question 1
Consider this equation.

−30(s−10)=−180


Correctly order the steps used to solve this equation.

(1 point)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Step 1:
Step 2:
Question 2
Solve for s.

−30(s−10)=−180

(1 point)
Responses

s = 16
s = 16

s = -4
s = -4

s = 50
s = 50

s = 70
s = 70
Skip to navigation

page 18 of 18

Answer 11

To solve the equation

\[ -30(s - 10) = -180, \]

let's go through the steps and then identify the correct order and final value of \( s \).

Step-by-step solution:

1. Step 1: Divide both sides of the equation by -30.
   \[ s - 10 = \frac{-180}{-30} \] This simplifies to:
   \[ s - 10 = 6 \]

2. Step 2: Add 10 to both sides of the equation.
   \[ s = 6 + 10 \] This simplifies to:
   \[ s = 16 \]

Correct Order of Steps

• Step 1: Divide both sides of the equation by -30.
• Step 2: Add 10 to both sides of the equation.

Final Answer for Question 2

Thus, the value of \( s \) is:

• \( s = 16 \).

You can fill in the steps and the answer accordingly!