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How do you graph and solve # |x-4|<9#?

Answer 1

#-5 < x < 13#

When working with absolute value inequalities, we need to remember that the absolute value function will return a positive value regardless of what lies within. For instance, if we have

#x=3#, #x# can be 3 or it can be #-3#. And so in our question we need to address this:

#abs(x-4)<9=>x-4 < pm9=> -9 < x-4 < 9#

We can now solve this by adding 4 to all sides:

#-9 < x-4 < 9#

#-9 color(red)(+4)< x-4color(red)(+4) < 9color(red)(+4)#

#-5 < x < 13#

We can graph this on a number line by placing hollow circles around #-5# and 13 (to indicate that all the points up to but not including #-5# and 13 are part of the solution) and then drawing a line connecting the two.

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Answer 2

Kennedy Adams

To graph and solve \( |x - 4| < 9 \), first, find the critical points by setting the expression inside the absolute value less than 9 and solving for \( x \). This yields two inequalities: \( x - 4 < 9 \) and \( x - 4 > -9 \). Solve each inequality separately to find the range of \( x \). The solution is the intersection of these two ranges. Graph the solution on a number line.

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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 graph and solve # |x-4|&lt;9#?

How do you graph and solve # |x-4|<9#?