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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:

7 answers

To solve the equation \( 4(3x - 2) = -24 \), we can follow these steps:

Step 1: Distribute \( 4 \) on the left side:
\[ 12x - 8 = -24 \]

Step 2: Add \( 8 \) to both sides:
\[ 12x = -16 \]

Step 3: Divide both sides by \( 12 \):
\[ x = -\frac{4}{3} \]

So, the ordered steps are:

  • Step 1: Distribute \( 4 \).
  • Step 2: Add \( 8 \) to both sides.
  • Step 3: Divide by \( 12 \).
Subtract 2 from both sides of the equation.
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 .

To correctly order the steps for solving the equation \( 4(3x - 2) = -24 \) using the options provided, we can outline the process as follows:

  1. Step 1: Multiply both sides of the equation by \( \frac{1}{4} \) (which is equivalent to dividing both sides by 4) to simplify: \[ 3x - 2 = -6 \]

  2. Step 2: Add 2 to both sides of the equation to isolate the term with \( x \): \[ 3x = -4 \]

  3. Step 3: Divide both sides of the equation by 3 to solve for \( x \): \[ x = -\frac{4}{3} \]

Using your provided steps, they correspond to:

  • Multiply both sides of the equation by 4. (This step is not necessary as we divide by 4 immediately.)
  • Add 2 to both sides of the equation. (Correct step to isolate \( x \).)
  • Divide both sides of the equation by 3. (Correct step to find \( x \).)

So in context: Step 1: Multiply both sides of the equation by \( \frac{1}{4} \) (but you can refer to the current step here).
Step 2: Add 2 to both sides of the equation.
Step 3: Divide both sides of the equation by 3.

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

Let's solve the equation \( 4(3x - 2) = -24 \) step by step to determine the correct value of \( x \).

  1. Distribute \( 4 \): \[ 4 \cdot 3x - 4 \cdot 2 = -24 \implies 12x - 8 = -24 \]

  2. Add \( 8 \) to both sides: \[ 12x - 8 + 8 = -24 + 8 \implies 12x = -16 \]

  3. Divide by \( 12 \): \[ x = -\frac{16}{12} = -\frac{4}{3} \]

Thus, the value of \( x \) is \( -\frac{4}{3} \), which corresponds to the choice:

  • x is equal to negative 4 thirds.
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
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page 18 of 18

To solve the equation \( -2(4+n) = 24 \), we need to follow these steps:

Order the Steps

Step 1: Distribute \( -2 \) to both terms inside the parentheses. \[ -8 - 2n = 24 \]

Step 2: Add \( 8 \) to both sides to isolate the term with \( n \). \[ -2n = 24 + 8 \implies -2n = 32 \]

Step 3: Divide both sides by \( -2 \) to solve for \( n \). \[ n = -\frac{32}{2} \implies n = -16 \]

Responses

Now, you can use the following choices to fill in the steps:

  • Step 1: Distribute \(-2\) (resulting in \(-8 - 2n = 24\))
  • Step 2: Add \( 8 \) to both sides (resulting in \(-2n = 32\))
  • Step 3: Divide both sides by \(-2\) (resulting in \(n = -16\))

Solve for \( n \)

The solution for \( n \) is:

  • n = -16.