Jill solves the equation 3(x−5)+2x=0

. Fill in the blanks for each step with the correct values:(3 points)

3x + (Blank) + 2x = 0
5x= (Blank)

x= (Blank)
Response area

1 answer

Let's solve the equation step by step and fill in the blanks.

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

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

  3. Combine like terms: \[ 3x + 2x - 15 = 0 \quad \text{which simplifies to} \quad 5x - 15 = 0 \]

Now we can fill in the blanks:

  • The first blank (after \(3x +\)) is -15 (the constant term from distributing).
  • The second blank involves the equation \(5x = 15\) (rearranging it to equal zero).

Thus, after solving for \(x\): \[ 5x = 15 \quad \Rightarrow \quad x = \frac{15}{5} \] This gives us \(x = 3\).

The values to fill in the blanks are:

  • First blank: -15
  • Second blank: 15
  • Third blank: 3

So the final responses are:

  • 3x + (-15) + 2x = 0
  • 5x = 15
  • x = 3