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How do you solve and graph #abs(x+1)<4#?

Answer 1

Eva Adamson

Please see below.

The numbers whose absolute values are less that #4# are between #-4# and #4#, so we need

#-4 < x+1 < 4#.

Subtracting #1# from each part gets us

#-5 < x < 3#

The solution set is #(-5,3)#.

To graph, put an open circle at #-5# and another at #3#. Connect them with s line segement.

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Answer 2

Julia Adams

To solve and graph the inequality ( |x + 1| < 4 ), you first solve the equation ( |x + 1| = 4 ) to find the boundary points, and then determine the interval(s) where the inequality is true.

The equation ( |x + 1| = 4 ) has two solutions: ( x = 3 ) and ( x = -5 ).

Now, since the inequality is ( |x + 1| < 4 ), it means that ( x ) can be any value that is less than 3 and greater than -5.

So, the solution to the inequality is ( -5 < x < 3 ).

To graph this on a number line, you plot an open circle at -5 and 3, and shade the region between them.

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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 and graph #abs(x+1)&lt;4#?

How do you solve and graph #abs(x+1)<4#?