10. Jill solves the equation 3(x−5)+2x=0

Question

. 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)

-15, 15, -3, 1, 5, -5, -1, 3

Answer 1

To solve the equation \(3(x-5) + 2x = 0\), let's go through each step.

1. Distributing \(3(x - 5)\): \[ 3(x - 5) = 3x - 15 \] Therefore, we can write: \[ 3x + (-15) + 2x = 0 \] The response for the first blank is \(-15\).

2. Combining like terms: \[ 3x + 2x = 5x \] So we have: \[ 5x - 15 = 0 \] The response for the second blank is \(15\).

3. Solving for \(x\): \[ 5x = 15 \] Dividing each side by \(5\): \[ x = 3 \] The response for the third blank is \(3\).

Putting together the answers:

1. \(-15\)
2. \(15\)
3. \(3\)