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

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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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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.

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.

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.

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