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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)

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

x= (Blank)

1 answer

Let's solve the equation step-by-step.

Starting with: \[ 3(x−5)+2x=0 \]

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

Now, we can fill in the blanks:

First Blank: -15 (the result after distributing)

Thus, we have: \[ 3x - 15 + 2x = 0 \]

  1. Combine like terms: \[ (3x + 2x) - 15 = 0 \] \[ 5x - 15 = 0 \]

Now, we can fill in the second blank:

Second Blank: 15 (the number after moving 15 to the other side)

Thus, we have: \[ 5x = 15 \]

  1. Solve for \(x\) by dividing both sides by \(5\): \[ x = \frac{15}{5} \] \[ x = 3 \]

Now, we can fill in the third blank:

Third Blank: 3 (the value of \(x\))

Putting it all together:

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