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How do you solve the inequality #abs(3x+5)+2<1# and write your answer in interval notation?

Answer 1

See a solution process below:

First, subtract #color(red)(2)# from each side of the inequality to isolate the absolute value function while keeping the inequality balanced:

#abs(3x + 5) + 2 - color(red)(2) < 1 - color(red)(2)#

#abs(3x + 5) + 0 < -1#

#abs(3x + 5) < -1#

The absolute value function takes any number and transforms it into its non-negative form. Therefore, the result of an absolute value function cannot be negative and therefore cannot be #color(red)(< -1)#.

So, there is no answer to this question. Or, the answer is the empty or null set: #{O/}#

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Answer 2

Kennedy Adams

To solve the inequality ( |3x + 5| + 2 < 1 ) and write the answer in interval notation:

Subtract 2 from both sides to isolate the absolute value term: ( |3x + 5| < -1 ).
Since an absolute value cannot be negative, there are no solutions for this inequality.
Thus, the solution set is the empty set, denoted by ( \emptyset ), and in interval notation, it is represented as ( \emptyset ).

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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 inequality #abs(3x+5)+2&lt;1# and write your answer in interval notation?

How do you solve the inequality #abs(3x+5)+2<1# and write your answer in interval notation?