To solve the inequality \( 9x + 15 \geq 51 \) and graph the solution, Eric would go through the following steps in order:
-
Subtract 15 from both sides: \[ 9x + 15 - 15 \geq 51 - 15 \] This simplifies to: \[ 9x \geq 36 \]
-
Divide both sides by 9: \[ \frac{9x}{9} \geq \frac{36}{9} \] This simplifies to: \[ x \geq 4 \]
-
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.
-
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.