Eric is solving the inequality 9x+15≥51

Question

and graphing the solution. Which of the following describes his steps?(1 point)
Responses

1.Subtract 15 from both sides of the inequality.
Divide both sides of the inequality by 9.
Plot the point given in the solution on the number line with a closed circle.
Shade to the right of the point on the number line.
Subtract 15 from both sides of the inequality. Divide both sides of the inequality by 9. Plot the point given in the solution on the number line with a closed circle. Shade to the right of the point on the number line.

2.Subtract 15 from both sides of the inequality.
Divide both sides of the inequality by 9.
Plot the point given in the solution on the number line with a closed circle.
Shade to the left of the point on the number line.
Subtract 15 from both sides of the inequality. Divide both sides of the inequality by 9. Plot the point given in the solution on the number line with a closed circle. Shade to the left of the point on the number line.

3.Divide both sides of the inequality by 9.
Subtract 15 from both sides of the inequality.
Plot the point given in the solution on the number line with a closed circle.
Shade to the right of the point on the number line.
Divide both sides of the inequality by 9. Subtract 15 from both sides of the inequality. Plot the point given in the solution on the number line with a closed circle. Shade to the right of the point on the number line.

4.Divide both sides of the inequality by 9.
Subtract 15 from both sides of the inequality.
Plot the point given in the solution on the number line with a closed circle.
Shade to the left of the point on the number line.

Answer 1

To solve the inequality \( 9x + 15 \geq 51 \), we can follow these steps:

1. Subtract 15 from both sides: \[ 9x \geq 51 - 15 \] Which simplifies to: \[ 9x \geq 36 \]

2. Divide both sides by 9: \[ x \geq \frac{36}{9} \] Which simplifies to: \[ x \geq 4 \]

3. The solution \( x \geq 4 \) means that on a number line, we will plot the point 4 with a closed circle (indicating that 4 is included in the solution) and shade to the right to indicate all values greater than or equal to 4.

Based on these steps, the correct response is:

Option 1:

• Subtract 15 from both sides of the inequality.
• Divide both sides of the inequality by 9.
• Plot the point given in the solution on the number line with a closed circle.
• Shade to the right of the point on the number line.