How do you solve #-3- 2| 4x - 5| \geq 1#?

1 Answer
AA_123
Apr 17, 2017

This problem has no solution

Explanation:

#-3-2|4x-5|>=1#

Add #3# to both sides

#cancel(-3color(blue)(+3))-2|4x-5|>=1color(blue)(+3)#

#-2|4x-5|>=4#

Divide both sides by #-2#, when you are dividing or multiplying by a negative number in an inequality, you must flip the inequality sign

#(cancel(-2)|4x-5|)/cancel(color(blue)(-2))color(red)(<=)4/color(blue)(-2)#

#|4x-5|<=-2#

And this inequality is false, because there's no such absolute value that outputs a negative number (a number #<0#) "in this case it is #(<-2)#", so this inequality has no solution.

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