1/2|6y-9| +5 is < or = 2

Question

i solved it and got two fractions but the answer is 0 can anyone explain?

btw this is absolute value inequality.

Answer 1

1/2|6y-9|+5 <= 2

1/2|6y-9|<=-3

multiply by 2 making the signs switch

|6y-9|>=-6
Since it's absolute value, do this:

6>=6y-9>=-6

15>=6y>=3

5/2 >= y >= 1/2

Answer 2

Jen was right up to where she multiplied by +2 and switched the inequality sign.

the sign only switches when multiplying or dividing by a negative number so it should have been

|6y-9| ≤ -6

at this point we have a "violation" of the definition of absolute value.
by definition the absolute value of anything has to be ≥ 0

So there is no solution.

Lyne , you said the answer was zero, it is not.
try subbing it in, it won't work, no number works.

Answer 3

ohh okay thanks so much that makes sense!

thanks again =)haha