Final answer:
To evaluate the expression x = 0.5x - 8 for x = 0.0216 and x = -0.0224, calculate 0.5(0.0216) - 8 = -7.9892 and 0.5(-0.0224) - 8 = -8.0112 respectively. Additionally, when working with positive and negative numbers, ensure to change the signs appropriately to conduct correct mathematical operations.
Step-by-step explanation:
To evaluate the expression for x = 0.5x - 8, it seems we need to handle two separate values for x, 0.0216 and -0.0224. Let’s evaluate the expression for both:
Using x = 0.0216:
0.5(0.0216) - 8 = (0.5 * 0.0216) - 8 = 0.0108 - 8 = -7.9892
Using x = -0.0224:
0.5(-0.0224) - 8 = (0.5 * -0.0224) - 8 = -0.0112 - 8 = -8.0112
For additional context, another part of the question suggests using the approximation that x << 0.200, which allows for simplifying certain expressions assuming x has a negligible effect compared to 0.200.
Examples on Adjustment with Signs
When handling operations with positive and negative signs, consider the following examples:
5 - (+3) = 5 - 3 = 2. Notice how the + sign before the 3 is changed to a - sign before performing the operation.
Another example is 2 - (-6) = 2 + 6 = 8, where the - sign before 6 is changed to a + sign.
It's also worth noting the importance of the order of the operations on some calculators and the use of special keys such as the Shift or second function key to enter certain functions like 10*.