There are 2 solutions to this question. Let's get the basic one first. Then we'll discuss what's going on.
-2 * abs(3x - 6) + 2 < 1 Subtract 2 from both sides.
-2 * abs(3x - 6) < 1 - 2
-2 * abs(3x - 6) < - 1 Divide by - 2 Be very careful with this. Something happens.
abs (3x - 6) > -1/-2 Did you notice that < changed to > ? That is the critical part of this question. If you miss this, you miss the whole thing.
abs(3x - 6) > 1/2 Now this is the basic part of the equation. The first answer is
3x - 6 > 1/2 Add 6 to both sides.
3x > 6 + 1/2
3x > 6 1/2 or 13 / 2 Divide by 3
x > 13/2 // 3/1
x > 13/2 * 1/3
x> 13/6 That is not one of your answers but we must find the other one anyway. Perhaps it is one of the listed answers.
3x - 6 > - 1/2 Another trick of inequalities. The basic "inequality" on the right is changed to a minus.
3x > 6 - 1/2
3x > 5 1/2
3x > 11/ 2 Now divide by 3
x > 11/(2*3)
x > 11/6
That answer is present in your list your list but this is another one of your trick questions. (Who gives these things out?)
It only looks like the answer is there to include 11/6 itself is not part of the possible answers. Anything above 11/6 or 13/6 will work.
What a nasty piece of work. 15/7 works and so does 11/5. This question has more tricks in it than a circus magician! But you have to go back to 13/6. Both of these answers have to exceed 13/6 which they both do.
