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How do you solve the absolute value inequalities #abs(x+4)<0#?

Answer 1

By solve the inequality, I assume you mean solve for #x#. In general you can only solve an equation or inequality for "something",

For the given inequality: #abs(x+4)<0# Note that #abs("anything")>=0# (it's basic to the definition of absolute value)

Therefore there is no value of #x# for which this inequality is true.

In set notation #x = phi " (the null set) "#

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Answer 2

Nathan Axel

The absolute value of any real number is always non-negative. Therefore, the inequality ( |x + 4| < 0 ) has no solutions in the set of real numbers.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve the absolute value inequalities #abs(x+4)&lt;0#?

How do you solve the absolute value inequalities #abs(x+4)<0#?