Another interval notation problem?

Question

Solve the inequality and express the solution set using interval notation.

-12(x-4) +3 > 4x - 4 - 5x

Do not convert fractions to decimal form.
Express your answer in interval notation. Inequalities will not be accepted.

heres another one as well thanks for the help
-6(17x+3)<-3(17x-3)

Answer 1

(-infty, 5)

Answer 2

1)
First combine like terms and simplify:

-12(x - 4) + 3 > 4x - 4 - 5x
-12x + 48 + 3 > -4 - x
-12x + 51 > -4 - x
55 > 11x
x < 5

Now, write in interval notation. Since "x" is less than 5, it's everything less than 5, all the way down to negative infinity. Since its not equal to 5 though, use parentheses, no brackets:

( -infinity , 5)


2)
-6(17x + 3) < -3(17x - 3)
-102x - 18 < -51x + 9
-27 < 51x
x> -27/51
x > -9/17

( -9/17 , infinity)

Try to use this to do a couple on your own. They get easier as you go.

Answer 3

Ya work all these out the same way. Solve for x like a regular equation (or inequality in this case), then convert to interval notation using the simple rules:

http://id.mind.net/~zona/mmts/miscellaneousMath/intervalNotation/intervalNotation.html
http://en.wikipedia.org/wiki/Interval_notation

-12x + 51 > -x + -4
0 > 11x - 55
55 > 11x
5 > x

(-infinity, 5)

Answer 4

-12(x - 4) +3 > 4x - 4 - 5x
-12x + 48 + 3 > -x - 4
-12x + 51 > -x - 4
-11x > -55
x < 5

(-infinity,5)

--------------------------------

-6(17x + 3) < -3(17x - 3)
-102x - 18 < -51x + 9
-51x < 27
x > (-9/17)

((-9/17),+infinity)