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inequality in interval notation:

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1 Answer

Let's start with definition of the absolute value:
1.  lxl = x ,  if x ≥ 0 {for example l5l = 5}
2.  lxl = -x , if x < 0 {     l-5l = -(-5) = 5}
and don't forget: if you multiply or divide both sides of inequality by negative number, you have "to switch" sign of inequality to opposite. For example -5x > 10 ---> x < -2
~~~~~~~~~~~
 -7 - 2(l7x - 5l) > -9 
+7                     +7
      -2 l7x - 5l > -2
  -2/-2 l7x - 5l > -2/-2
          l7x - 5l < 1
1. if (7x - 5) ≥ 0 , then 7x - 5 < 1 ---> x < 6/7
2. If (7x - 5) < 0 , then -(7x - 5) < 1 ---> 7x - 5 > -1 ---> x > 4/7
The answer is: any  number from an interval (4/7 , 6/7)