Question

Jill solves the equation 3(x−5)+2x=0
Fill in the blanks for each step with the correct values:

Answer 1

To solve the equation \( 3(x - 5) + 2x = 0 \), we can follow these steps and fill in the blanks accordingly:

1. **Distribute the \(3\)**:
\[
3(x - 5) = 3x - 15
\]
So we can rewrite the equation as:
\[
3x - 15 + 2x = 0
\]

2. **Combine like terms**:
Adding \(3x\) and \(2x\):
\[
(3x + 2x) - 15 = 0
\]
This simplifies to:
\[
5x - 15 = 0
\]

3. **Add \(15\) to both sides**:
\[
5x - 15 + 15 = 0 + 15
\]
This simplifies to:
\[
5x = 15
\]

4. **Divide both sides by \(5\)**:
\[
\frac{5x}{5} = \frac{15}{5}
\]
This simplifies to:
\[
x = 3
\]

Thus, the equation \( 3(x−5)+2x=0 \) is solved, and the final answer is \( x = 3 \).

So, if the blanks were meant to reflect the process steps, they could be:
- Step 1: \(3(x - 5)\) becomes \(3x - 15\)
- Step 2: Combine to get \(5x - 15 = 0\)
- Step 3: Add \(15\) to both sides to get \(5x = 15\)
- Step 4: Divide to find \(x = 3\)