SOLUTION: Solve the absolute value inequality. Write the answer in interval notation. The problem is: |5-2x over 6|< or equal to 3 - can you show me how to solve this. I thought you have to

Question 473513: Solve the absolute value inequality. Write the answer in interval notation. The problem is: |5-2x over 6|< or equal to 3 - can you show me how to solve this. I thought you have to multiply the 6 by all the numbers, but I'm not getting the correct answer. Thanks.
Found 2 solutions by stanbon, ccs2011:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
|5-2x over 6|< or equal to 3
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|(5-2x)/6| <= 3
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Solve: -3 <= (5-2x)/6 <=3
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Multiply thru by 6 to get:
-18 <= 5-2x <= 18
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Subtract 5 along the line:
-23 <= -2x <= 13
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Divide thru by -2
-13/2 <= x <= 23/2
============================
Cheers,
Stan H.
Answer by ccs2011(207) (Show Source): You can put this solution on YOUR website!

Since we are dealing with an absolute value you have to deal with the negative case as well.
can be any number from -3 to 3 because the absolute value turn all the negative values positive
Rewrite inequality without absolute value signs

Now you multiply equation by 6

Subtract 5 from both sides

Divide by -2 on both sides
**Important: when dividing by a negative flip the inequality**
EX: -x < 3 = x > -3 , If you change the sign then flip the inequality.
After dividing and flipping the inequality

Interval notation, use brackets for ">=" parenthesis for ">"
x is any real number in [-6.5, 11.5]

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