Question
10. Jill solves the equation 3(x−5)+2x=0 . Fill in the blanks for each step with the correct values:(3 points)
Answers
Answered by
GPT-4o mini
To solve the equation \( 3(x-5) + 2x = 0 \), let's go through it step by step. We'll fill in each part of the process:
1. **Distribute the \(3\)**:
\(3(x-5) = 3x - 15\)
Therefore, the equation becomes:
**Step 1:** \(3x - 15 + 2x = 0\)
2. **Combine like terms**:
\(3x + 2x = 5x\)
So, the equation simplifies to:
**Step 2:** \(5x - 15 = 0\)
3. **Add 15 to both sides**:
\(5x = 15\)
**Step 3:** \(5x = 15\)
4. **Divide by 5**:
\[x = \frac{15}{5} = 3\]
**Step 4:** \(x = 3\)
So, the completed steps are:
1. \(3x - 15 + 2x = 0\)
2. \(5x - 15 = 0\)
3. \(5x = 15\)
4. \(x = 3\)
1. **Distribute the \(3\)**:
\(3(x-5) = 3x - 15\)
Therefore, the equation becomes:
**Step 1:** \(3x - 15 + 2x = 0\)
2. **Combine like terms**:
\(3x + 2x = 5x\)
So, the equation simplifies to:
**Step 2:** \(5x - 15 = 0\)
3. **Add 15 to both sides**:
\(5x = 15\)
**Step 3:** \(5x = 15\)
4. **Divide by 5**:
\[x = \frac{15}{5} = 3\]
**Step 4:** \(x = 3\)
So, the completed steps are:
1. \(3x - 15 + 2x = 0\)
2. \(5x - 15 = 0\)
3. \(5x = 15\)
4. \(x = 3\)