SOLUTION: What is the compound inequality for |6x-5| < 10

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Question 683951: What is the compound inequality for |6x-5| < 10
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Learn the four ways to eliminate absolute value bars:

1.        abs%28matrix%282%2C1%2C++ALGEBRAIC%2CEXPRESSION%29%29%22%22%3C%22%22K  is equivalent to this:  " -K%22%22%3C%22%22matrix%282%2C1%2CALGEBRAIC%2CEXPRESSION%29%22%22%3C%22%22K "

2.        abs%28matrix%282%2C1%2C++ALGEBRAIC%2CEXPRESSION%29%29%22%22%3C=%22%22K  is equivalent to this:  " -K%22%22%3C=%22%22matrix%282%2C1%2CALGEBRAIC%2CEXPRESSION%29%22%22%3C=%22%22K " 

3.        abs%28matrix%282%2C1%2C++ALGEBRAIC%2CEXPRESSION%29%29%22%22%3E%22%22K  is equivalent to this: "  matrix%282%2C1%2CALGEBRAIC%2CEXPRESSION%29%22%22%3C%22%22-K   %22OR%22   matrix%282%2C1%2CALGEBRAIC%2CEXPRESSION%29%22%22%3E%22%22K "

4.        abs%28matrix%282%2C1%2C++ALGEBRAIC%2CEXPRESSION%29%29%22%22%3E=%22%22K  is equivalent to this: "  matrix%282%2C1%2CALGEBRAIC%2CEXPRESSION%29%22%22%3C=%22%22-K   %22OR%22   matrix%282%2C1%2CALGEBRAIC%2CEXPRESSION%29%22%22%3E=%22%22K "

Yours is case 1:

   |6x-5| < 10 is equivalent to

     -10 < 6x-5 < 10

We solve for x in the middle:

Add +5 to all three sides like this:

     -10 < 6x-5 < 10
      +5     +5   +5
      -5 < 6x   < 15

Dow divide all three sides by 6

      %28-5%29%2F6 < x  < 15%2F6

The fraction on the right reduces to 5%2F2

      %28-5%29%2F6 < x  < 5%2F2

In interval notation that is:

         %28matrix%281%2C3%2C%0D%0A%0D%0A-5%2F6%2C%22%2C%22%2C5%2F2%29%29
   


Edwin