Posted by **Shreya** on Tuesday, January 17, 2012 at 7:14pm.

the absolute value function

g(x) = |5-x| can be written as a piecewise function. the piecewise function which represents g(x) is

this have to be g(x) = x-5 if x be greater to or equal to five. and the negative piece have to be 5-x. does it matter if i write -5+x instead of 5-x?

which of following is root of equation |3x-1| = -5

i get -4/3 for this.

- math-calculus -
**Damon**, Tuesday, January 17, 2012 at 7:44pm
from x = -oo to x = 5

g = -5 + x

from x = 5 to x = oo

g = x - 5

3x-1 = -5

3 x = -4

x = -4/3

- math-calculus -
**Shreya**, Tuesday, January 17, 2012 at 7:50pm
thank you for the 3x-1 = -5 it says in back of book that there are no roots of the equation |3x-1| = -5 and i not see how that be possible.

- math-calculus -
**Reiny**, Tuesday, January 17, 2012 at 9:32pm
By definition

| anything | has to be a positive number or at least zero

so |3x-1\ = -5 would contradict the very definition of absolute value,

So without even showing a single step, we can say that there is no solution.

if you verify your answer of -4/3, ...

LS = |3(-4/3) - 1|

= | -5|

= +5

RS = -5

LS ≠ RS , so .... no solution

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