Eric is solving the inequality 9x+15≥51

Question

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

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.
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.

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.

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.

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.

Answer 1

Let's solve the inequality \(9x + 15 \geq 51\) step by step.

1. Subtract 15 from both sides: \[ 9x + 15 - 15 \geq 51 - 15 \quad \Rightarrow \quad 9x \geq 36 \]

2. Divide both sides by 9: \[ \frac{9x}{9} \geq \frac{36}{9} \quad \Rightarrow \quad x \geq 4 \]

3. Graph the solution on a number line:

   • The solution can be represented as \(x \geq 4\).
   • This means we plot a closed circle at \(4\) (indicating that \(4\) is included in the solution).
   • Since the inequality is \( \geq \), we shade to the right of the \(4\) on the number line to indicate all values greater than or equal to \(4\).

Given these steps, the correct response would be:

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.