Jill solves the equation 3(x−5)+2x=0 . Fill in the blanks for each step with the correct values:(3 points)

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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