What is the absolute value for |10p - 4| < 34 ?

What is the absolute value for |10p-4| < 34 ?

\(| 10p-4 |<34 \)

\(| p | <\frac{34+4}{10}\)

\(| p | < 3.8\)

\(L = \{| p | \in \mathbb| \mathbb R | <3.8\}\)

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We will actually have an open interval solution here that will lie between two values

l 10p - 4  l  < 34    set the equation equal

l 10p - 4 l  =  34

This says that

10p - 4  = 34                            and                    10p - 4 = -34

add 4 to both sides                                           

10p = 38                                                          10p = -30

divide both sides by 10

p = 3.8                                                                 p  = - 3

The solutions will occur between these two values....so     -3 < p < 3.8