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

Answer 1

To solve the equation \( 3(x - 5) + 2x = 0 \), let's go step by step filling in the blanks.

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

So, we have:

• In the first response area: -15

2. Combine like terms (the \( x \) terms): \[ 3x + 2x = 5x \]

So, we have:

• In the second response area: -15

3. Now the equation looks like: \[ 5x - 15 = 0 \]

4. To isolate \( x \), add \( 15 \) to both sides: \[ 5x = 15 \]

So, we have:

• In the third response area: 15

5. Finally, divide by \( 5 \) to solve for \( x \): \[ x = 3 \]

So, we have:

• In the fourth response area: 3

Putting it all together, the filled responses are:

• For \( 3x + _ + 2x = 0 \): -15
• For \( 5x = _ \): 15
• For \( x = _ \): 3