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Solving Absolute Value Inequalties with Less Than

Here's another one:

Solve | 5x - 1 | < 9


A number line showing that 5x - 1 lives between -9 and 9
 

-9 < | 5x - 1 | < 9 ... add 1 to all three parts ... -8 < 5x < 10 ... divide all three parts by 5 ... - ( 8 / 5 ) < x < 2 ... ( - ( 8 / 5 ) , 2 ) ... Done!

TRY IT:

Solve | 2x - 3 | is less than or equal to 1

 

Solve*     3 | x - 1 | + 2 < 8

*Get the absolute value blob alone first!

See anything wrong with this guy?

| x - 2 | is less than or equal to -4 ... How can a distance be less than a -4? ... the 4 is negative!

It can't!  So, get your finger out of your nose and watch out for these!

(Btw, your response to this should have been, "Hey, my fingers are in my ears, not my nose!")