Answer:
To find the minimum and maximum acceptable ball masses, we can set up an absolute value equation based on the given information.
Let x be the actual mass of the soccer ball in kilograms. The recommended mass is 0.43 kilograms, and it is allowed to vary by up to 20 grams (0.02 kilograms).
The absolute value equation can be written as:
| x - 0.43 | ≤ 0.02
To solve this equation, we can split it into two cases:
Case 1: x - 0.43 ≤ 0.02
Solving for x, we have:
x ≤ 0.43 + 0.02
x ≤ 0.45
Case 2: -(x - 0.43) ≤ 0.02
Simplifying the inequality, we get:
- x + 0.43 ≤ 0.02
- x ≤ 0.02 - 0.43
- x ≤ -0.41
Dividing both sides of the inequality by -1, the direction of the inequality sign changes:
x ≥ 0.41
Thus, the solution to the absolute value equation is:
0.41 ≤ x ≤ 0.45
Therefore, the minimum acceptable ball mass is 0.41 kilograms, and the maximum acceptable ball mass is 0.45 kilograms.