Final answer:
The situation where the difference between the areas of two figures is less than or equal to 10 square units is represented by the inequality |A - B| ≤ 10. This expression uses absolute value to account for which figure is larger and includes all the values within a 10-square-unit difference. The area between -10 and 10 on a number line, inclusive of the endpoints, graphically represents the inequality.
Step-by-step explanation:
To represent the situation where the difference between the areas of two figures is less than or equal to 10 square units, you can use an absolute value inequality. Let A and B represent the areas of the two figures. Then, the inequality that describes this situation can be expressed as |A - B| ≤ 10.
This inequality states that no matter which figure has the larger area, the magnitude of the difference in their areas should not exceed 10 square units. The absolute value is used because the difference could be negative if B is larger than A, but we are only interested in the magnitude of the difference, not the direction.
To graph this inequality on a number line:
- Place points at A - B = -10 and A - B = 10, which are the boundaries of the inequality.
- Since the inequality is ≤ (less than or equal to), you will shade the region between these two points, including the endpoints themselves.
This shaded area represents all the possible values of A and B that satisfy the inequality, meaning that the difference in areas is at most 10 square units.