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

Answer 1

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. \(x = 3\)