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we have negative numbers with a relation so *we have to be careful* the "fast way" is multiply both sides by -1 and *switch the relation operator* the slow (but easy to do) way is add +3 to both sides then add +3 | x-5| to both sides either way, what do you get?
do it in steps -3 | x-5| < -3 which way do you want to do it? fast way or slow way?
fast way of course!
fast way: multiply both sides by -1 *flip the relation operator*
would it be 3/x-5/<3 ??
you did step 1 ok. but step 2 means you change < to > or if you had > you would change it to < or \(\le\) would be changed to \( \ge\) that is the "flip" part
yes. the problem with the fast way is you have to remember to flip the operator... if you don't have a good memory for "details", the slow way is safer (one less rule to remember) so now you have 3 | x-5| > 3 it is safe to divide both sides by 3. you get | x-5 | > 1
with absolute value problems we *always* have two conditions either x-5 is positive , in which case , drop the | | or x-5 is negative, in which case we replace the | | with -1*(x-5)
let's do the x-5 is positive condition. we have x-5 > 1 now add +5 to both sides
now do the x-5 is negative case. can you do that one?
yes(hopefully)! So i got x<4
looks good. x<4 or x>6 are the solutions put an open circle at 4. the open (not solid , filled in) means 4 is not part of the answer, but we can get as close to 4 as we want (without being exactly 4) and x smaller than 4. all numbers smaller (to the left) of 4 are part of the solution as it would take a long time to draw a line showing all of the numbers, we use an arrow tip to show the answer includes all numbers the arrow points towards.
and then do the same for x> 6 open circle at 6 an arrow pointing which way ??
gotcha:) So, the arrows will be pointing in opposite direction x-------->6 and x<----------4 the arrows is showing thee way it'll go:)
yes. one last point: put the answers on the same number line
kk. Hold on...|dw:1439061932632:dw|
yes. looks good. for your teacher, make sure the "tick mark" for the 4 is clearly marked (in your graph it is not clear which tick mark is the 4)
Will do:)! Thanks again phi<3<3