Algebra help please

Question

Solve for the variable and express the answer in set notation: |5x-4|=11

 

i have to show work.

 

please explain this to me.

Answer 1

To "solve" means to find the value(s) of x for which the equation is true.

 

For:

   |x| = a

  either:     x = a        or      -x = a            [note:  that's what absolute value means]

 

In this problem, |5x-4|=11, either:

  (5x-4) = 11         or      -(5x-4) = 11

   5x = 15                       -5x = 7

    x = 3                           x = -7/5

 

Set notation lists those possible values:

     { -7/5,  3 }

 

Answer 2

Hi Carolyn

 

|5x-4|=11

 

We set this up as follows:

 

-11 = 5x-4 = 11    Notice the 5x-4 is set equal to -11 and +11 without the absolute value sign

 

Now to solve

-11 = 5x-4 = 11

+4       +4     +4

 

-7 = 5x = 15

÷5   ÷5    ÷5

 

-7/5 = x = 3

 

So, 

x = -7/5 and 3

 

In set notation

x = {-7/5, 3}