Final answer:
To solve and graph the absolute value inequality |3x + 15% < 9, subtract 15%, divide by 3, and draw a number line graph.
Step-by-step explanation:
To solve and graph the absolute value inequality |3x + 15% < 9, follow these steps:
- Step 1: Subtract 15% from both sides of the inequality:
|3x| < 9 - 15%
|3x| < 9 - (0.15)(9)
|3x| < 9 - 1.35
|3x| < 7.65 - Step 2: Divide both sides of the inequality by 3:
|x| < 7.65/3
|x| < 2.55 - Step 3: We now have two inequalities to consider:
x < 2.55 or x > -2.55 - Step 4: Graph the solution on the number line. Since the absolute value represents the distance from zero, the solution is all values on the number line that are less than 2.55 units away from zero. Therefore, draw an open circle at -2.55 and shade the region to the left of -2.55, and another open circle at 2.55 and shade the region to the right of 2.55.