Paolo is solving the inequality \( 15+2 x>31 \). To solve the inequality, he begins by solving the equation as shown. Which number line represents the solution to the inequality?

To solve the inequality \( 15 + 2x > 31 \), we first isolate \( x \). 1. Subtract 15 from both sides: \[ 2x > 31 - 15 \] \[ 2x > 16 \] 2. Next, divide both sides by 2: \[ x > \frac{16}{2} \] \[ x > 8 \] The solution to the inequality is \( x > 8 \). To represent this solution on a number line: - You would draw an open circle at the number 8 (indicating that 8 is not included in the solution). - Then, you would shade the line to the right of 8 to indicate that all numbers greater than 8 are included in the solution. So, the correct number line representation for the solution \( x > 8 \) would show an open circle at 8 and shading to the right.