Question

Eric is solving the inequality and graphing the solution.

9x+15≥51


Correctly order the steps he used.

Answer 1

To solve the inequality \( 9x + 15 \geq 51 \) and graph the solution, Eric would go through the following steps in order:

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

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

3. **Graph the inequality on a number line**:
- Draw a number line.
- Place a closed dot on 4 (indicating that 4 is included in the solution since it’s a "greater than or equal to" inequality).
- Shade the line to the right of 4 to show all numbers greater than 4 are included in the solution.

4. **Write the solution in interval notation**:
The solution can be expressed as:
\[
[4, \infty)
\]

This ordered list of steps outlines the correct procedure Eric would follow to solve the inequality and graph the solution.