How do you solve and graph #abs(3h-3)<12#?

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Answer 1 · 2017-07-14T15:28:22

#-5 < h < +5#

Full explanation given

#color(blue)("Preamble")#

The | | are special brackets. They indicate that whatever is inside them is to be considered as positive.

To emphasize this point, suppose that instead of the < we had = giving us:

#|3h-3|=12#

This would have to be the same as

#|+-12|=+12#

So you would get 2 values for #h#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question")#

Given:#" "|3h-3|<12#

Treating the | | as behaving just like brackets factor out the 3

#3|h-1|<12#

divide both sides by 3

#|h-1|<4#

Just for the moment consider this as

#h-1<4#

add 1 to both sides

#h<5#

Now put back the 'absolute' brackets

#|h|<5#

Write as

#|+-h|<5#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

For this to work we have the condition:

#-5 < h < +5#

The plot of this on the number line looks like this:-
Tony B

The 'hollow blobs' on the and of the red line (above) indicate that the actual values of 5 and -5 are not included.

The feasible region for #x and y# is the shaded area in the graph below.
Tony B