Final answer:
The inequality |2x-16| ≤0 has only one solution, x = 8, because the absolute value of any non-zero number is always positive. No complex manipulation is necessary; simply set the inside of the absolute value to zero and solve.
Step-by-step explanation:
To solve the inequality |2x−16| ≤0, we have to recognize the properties of absolute values. The expression within the absolute value symbols can only be zero because any positive or negative value would result in a value greater than zero after applying the absolute value. Therefore, the only solution for this inequality is when the expression inside the absolute value equals zero. Solving 2x−16 = 0 gives us x = 8 as the only solution.
It is important to note that any manipulation of inequalities, such as squaring both sides or using quadratic equations, should maintain the inequality's direction unless we multiply or divide by a negative number, which would flip the inequality. In this case, we did not need to use these methods, as the nature of the absolute value provides a straightforward solution.
A real-life application of using inequalities is to compare two metric measurements. For example, it's like saying one person's height is less than or equal to another person's height, and this comparison helps to understand the relative differences between the two measurements.