Question

Solve the inequality -3|6-x|less than -15 for x.
Graph the solution.

Answer 1

-3|6-x|/-3 < -15/-3
=
|6 - x|< 5
=
-5 < |6-x| < 5
-5-6 <|-x| < 5 -6
-11/-1<-x/-1< -1/-1
flip the signs as you are dividing by a negative
thus
11 > x > 1

thus you have that x is less than 11 but greater than 1
so
the functions domain on the real line is as follows

Answer 2

Note that thsi function goes infinitely close to 11 and 1 but never reaches those numbers

Answer 3

thanks :)

Answer 4

to graph this remember you have two different functions, remember that the output of an abosolutve value always has to be positive.

-3(-6+x)
and
-3(6 - x)

Thus what ever is in the brackets has to be negative, a (-)(-) = + so check where what is inside the brackets is

-6 + x = 0
x = 6 and we notice that if we go any higher than 6 the function will be give us a positive number and if we put anything in lower than 6 we get a negative (which we want).
thus we have that for the first equation
-3(-6+x), x < 6
we do the same for the second equation and we get
-3(6 - x), x > 6

We notice also that if x = 6 the function is 0 because -3(0) = 0

so now you just sub the corresponding x values into the specific equation know the domain of the function is (1,11)

Answer 5

I hope this helps you with absolute values they are pretty intimidating at first, at least I felt that way when I first encountered them.