How do you solve an absolute value equation?
describe all numbers x that are at a distance of 1/4 from the number −6. express this using absolute value notation.
create an absolute value inequality that has no solution?

The distance between two real numbers is the absolute value of their difference, . So the statement "all that are 1/4 away from -6" is captured in the equation

or

To solve, you can use the definition of absolute value: if is not negative, then ; otherwise, .

So there are two cases to consider:

1. Suppose . Then , and the equation reduces to

2. Suppose . Then and

, so the two solutions we found are correct because both and are indeed 1/4 away from -6.

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For the question regarding inequality, you know that the absolute value must return a non-negative number. In other words, there is no such that .

80 the answer is 80

step-by-step explanation:

m

step-by-step explanation: