Jill solves the equation 3(x−5)+2x=0

Question

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 \(x = 3\)