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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

1 answer

Let's solve the equation step by step in order to fill in the blanks correctly.

  1. Start with the original equation: \( 3(x - 5) + 2x = 0 \)

  2. Distribute \( 3 \) into \( (x - 5) \): \( 3x - 15 + 2x = 0 \)

  3. Combine like terms: \( 3x + 2x - 15 = 0 \) So, we combine \( 3x + 2x \) to get: \( 5x - 15 = 0 \)

Now, we can fill in the blanks based on what we found:

  1. The complete equation is: \( 3x - 15 + 2x = 0 \) Fill in the blank: \(-15\)

  2. After combining like terms: \( 5x = 15 \) Fill in the blank: \(15\)

  3. To solve for \( x \): Divide both sides by \( 5 \): \( x = 3 \) Fill in the blank: \(3\)

Putting it all together:

  • \( 3(x - 5) + 2x = 0 \) becomes \( 3x - 15 + 2x = 0 \)
  • Combine the terms to get \( 5x - 15 = 0 \)
  • Solving gives \( x = 3 \)

Final responses for each blank:

  1. -15
  2. 15
  3. 3