SOLUTION: Solve for q |-6q+9| < 15

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Question 998995: Solve for q |-6q+9| < 15
Found 3 solutions by josgarithmetic, ikleyn, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
This is the same as expecting -6q%2B9 to be between -15 and 15, or as a mathematical inequality statement, -15%3C-6q%2B9%3C15. Easier to think of it this way. Solve now.

-5%3C-2q%2B3%3C5
-8%3C-2q%3C2
highlight%284%3Eq%3E1%29

Answer by ikleyn(52891) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve for q: |-6q+9| < 15.
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To solve this absolute value inequality,  you should solve two systems of linear inequalities.  The first system is

system%28-6q+%2B+9+%3E=+0%2C%0D%0A-6q+%2B+9+%3C+15%29.

The second system is

system%28-6q+%2B+9+%3C+0%2C%0D%0A6q+-+9+%3C+15%29.

Then the union of solution sets to each system will be the solution of the given absolute value inequality.


Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

Solve for q |-6q+9| < 15
highlight_green%28-+1+%3C+q+%3C+4%29