My question regarding making absolute value fall in a particular range. In your book you gave two example (pg 149) and my question is what value should I consider as the end? is it the highest value or the (highest value+1) . Because in question#19 pg149 you consideed 181 to be the end, when 181 isn’t included! & what if the inequality symbol is less than or equal to, what should I do in that case?

If you’re doing the problem algebraically (recommended), it doesn’t matter what the inequality symbols is, as long as you’re consistent. Converting, say |w-162|<19 to 143<w<181 is algebraically exactly the same as converting |w-162|\leq 19 to 143\leq w \leq 181. Just take your cue from the question’s answer choices and use the same symbol the question does.

If you’re solving by plugging in, as I do first on pages 149 through 151, then it also doesn’t matter much as long as you’re able to keep track of whether the number you’re testing should be producing true inequalities or false ones.  I used 142 and 182 as examples just to make it a bit more obvious that those numbers SHOULD NOT produce true inequalities, although given the less-than symbol in play I could have used 143 and 181.

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