-7-2 |7 x-5| gt -9

## inequality in interval notation:

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# 1 Answer

Let's start with definition of the absolute value:

1.** l**x**l** = x , if x ≥ 0 {for example l5l = 5}

2. **l**x**l** = **-**x , if x < 0 { **
l**-5**l** = **-**(-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(**l**7x - 5**l**) > -9

+7 +7

-2 **l**7x - 5**l** > -2

-2/-2 **l**7x - 5**l** > -2/-2

**l**7x - 5**l** < 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)**

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