Which graph represents the solutions to the inequality |5x - 10| 15?

Question

please help me with this.

Answer 1

Serkan,  remember that the absolute value is the distance from zero.  Since distance is always positive, your absolute value is always positive.

 

|5x - 10| > 15

 

This means that 5x - 10 must be greater than or equal to 15 OR less than or equal to -15, since our value inside can be positive or negative.

 

Why? Let's take a look.

 

5x - 10 > 15.

       5x > 25

         x > 5

 

Let's check. We'll pick a number greater than 5, like 6.

 

5(6) - 10 > 15

  30- 10 > 15

         20 > 15.  True!

 

5x - 10 < -15

       5x < -5

         x < -1

 

Let's check again.  We'll pick -2.

 

5(-2) - 10 < -15

   -10 - 10 < -15.

           -20 < -15. Also true!

 

Hope this helps!