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

1 Answer
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.