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6. Put the steps in order to solve the equation: 3n+9+4n=2 (6 points) Explain your steps to get the next step and then your answer Step 1: to get: Step 2: to get: Step 3: to get:

9 answers

To solve the equation \(3n + 9 + 4n = 2\), we can break it down into clear steps:

Step 1: Combine like terms on the left side of the equation.

What to do: Add the coefficients of \(n\). \[ 3n + 4n = 7n \] Update the equation: \[ 7n + 9 = 2 \]

Step 2: Isolate the term with \(n\) by subtracting 9 from both sides.

What to do: Subtract 9 to move the constant term to the right side. \[ 7n + 9 - 9 = 2 - 9 \] Update the equation: \[ 7n = -7 \]

Step 3: Divide both sides by 7 to solve for \(n\).

What to do: Divide to get \(n\) by itself. \[ \frac{7n}{7} = \frac{-7}{7} \] Update the equation: \[ n = -1 \]

Final Answer:

The solution to the equation \(3n + 9 + 4n = 2\) is \(n = -1\).

7. Which equation has the same first step to solve as this equation: 2x+12−3x=27 (1 point) Responses 4x−17+2x=9 4 x minus 17 plus 2 x is equal to 9 2(x−5)+2x=10 2 times open paren x minus 5 close paren plus 2 x is equal to 10 2x+12=27 2 x plus 12 is equal to 27 2x+12=−3x−27

To determine which equation has the same first step to solve as the equation \(2x + 12 - 3x = 27\), we need to look at what that first step entails.

First Step of \(2x + 12 - 3x = 27\):

  1. Combine like terms on the left side of the equation.
    • \(2x - 3x = -x\)
    • This gives us: \(-x + 12 = 27\)

Now let's analyze each provided response to see which one also requires the same first step of combining like terms:

  1. Equation: \(4x - 17 + 2x = 9\)

    • Combine like terms: \(4x + 2x = 6x\)
    • This has the same first step.

  2. Equation: \(2(x - 5) + 2x = 10\)

    • The first step involves distributing \(2\) to \((x - 5)\) and does not involve combining like terms in the same way.

  3. Equation: \(2x + 12 = 27\)

    • There are no like terms to combine, so this does not have the same first step.

  4. Equation: \(2x + 12 = -3x - 27\)

    • This will also require moving \(3x\) to the left side, but it does not have like terms on the left side to combine directly.

Conclusion:

The equation that has the same first step to solve as \(2x + 12 - 3x = 27\) is:

Response: \(4x - 17 + 2x = 9\)

8. Using the Distributive Property as a good first step to solving the equation 7(5x+2)=−4(6−5x) , you could simplify this equation to get which of these choices?(1 point) Responses 5x+14=6+20x 5 x plus 14 is equal to 6 plus 20 x 35x+2=24−20x 35 x plus 2 is equal to 24 minus 20 x 35x+2=−24−5x 35 x plus 2 is equal to negative 24 minus 5 x 35x+14=−24+20x 35 x plus 14 is equal to negative 24 plus 20 x 35x+14=−24−20x

To solve the equation \(7(5x + 2) = -4(6 - 5x)\) using the Distributive Property, we will distribute the coefficients on both sides of the equation.

Distributing the Terms:

  1. Distribute on the left side: \[ 7(5x) + 7(2) = 35x + 14 \]

  2. Distribute on the right side: \[ -4(6) + (-4)(-5x) = -24 + 20x \]

Putting it All Together:

After performing the distribution, the equation simplifies to: \[ 35x + 14 = -24 + 20x \]

Now, let's match this with the provided responses:

  1. Response: \(5x + 14 = 6 + 20x\)

    • This does not match our result.

  2. Response: \(35x + 2 = 24 - 20x\)

    • This does not match our result (the constants are incorrect).

  3. Response: \(35x + 2 = -24 - 5x\)

    • This does not match our result.

  4. Response: \(35x + 14 = -24 + 20x\)

    • This matches our result.

  5. Response: \(35x + 14 = -24 - 20x\)

    • This does not match our result.

Conclusion:

The correct response after applying the Distributive Property is:

Response: \(35x + 14 = -24 + 20x\).

9. For the equation 2(x−5)=9−3x+6+8+3x+7 , the left side of the equation can be simplified using the Distributive Property, and the right side of the equation can be simplified by combining like terms. (2 points) 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. Simplify the left side of the equation: Response area Simplify the right side of the equation: Response area

To simplify the given equation \(2(x - 5) = 9 - 3x + 6 + 8 + 3x + 7\), we will follow the steps of applying the Distributive Property on the left side and then combining like terms on the right side.

Simplifying the Left Side:

Left Side:

  • We will apply the Distributive Property \(2(x - 5)\): \[ 2 \cdot x - 2 \cdot 5 = 2x - 10 \]

Simplified Left Side:
Response area: \(2x - 10\)

Simplifying the Right Side:

Right Side:

  • We have the expression \(9 - 3x + 6 + 8 + 3x + 7\).

  • First, we'll combine the constant terms: \[ 9 + 6 + 8 + 7 = 30 \]

  • Next, combine the like terms involving \(x\): \[ -3x + 3x = 0 \]

This leads us to: \[ 30 \]

Simplified Right Side:
Response area: \(30\)

Final Input:

  • Left Side Response Area: \(2x - 10\)
  • Right Side Response Area: \(30\)
10. Jill solves the equation 3(x−5)+2x=0 . Fill in the blanks for each step with the correct values:(3 points) 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. 3x+ Response area+2x=0 5x= Response area x= Response area

To solve the equation \(3(x - 5) + 2x = 0\), we'll follow these steps and fill in the blanks accordingly.

Step 1: Apply the Distributive Property

Distributing \(3\) across \((x - 5)\): \[ 3x - 15 + 2x = 0 \]

So now the equation looks like: \[ 3x + \text{Response area} + 2x = 0 \]

Response area: \(-15\)

Step 2: Combine like terms

Combine \(3x\) and \(2x\): \[ (3x + 2x) - 15 = 0 \implies 5x - 15 = 0 \]

So, we have: \[ 5x = \text{Response area} \]

Response area: \(15\) (adding \(15\) to both sides)

Step 3: Solve for \(x\)

Now, divide both sides by \(5\): \[ x = \frac{15}{5} \implies x = 3 \]

So, we fill in the last blank: \[ x = \text{Response area} \]

Response area: \(3\)

Summary of Responses

  • First Response area: \(-15\)
  • Second Response area: \(15\)
  • Third Response area: \(3\)