Question

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

Answer 1

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**