SOLUTION: Please solve these inequality problems .I'm having a hard time with the fractions 1) -1 > or = 1/4x 2) 1/2 > or = -1/6 -2/9x 3) 2/3x -3 < 1

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Question 50548This question is from textbook iintermediate algebra
: Please solve these inequality problems .I'm having a hard time with the fractions
1) -1 > or = 1/4x
2) 1/2 > or = -1/6 -2/9x
3) 2/3x -3 < 1
 This question is from textbook iintermediate algebra

Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
The easiest way to deal with fractions is to get rid of them by multiplying the entire inequality by a common factor:
.
1) -1 > or = 1/4x [Multiply each term by "4". This will get rid of the fraction]
4(-1 > = 1/4x)
(4)(-1)>=(4)(1/4)x [Cancel wherever possible]
-4>=x
.
2) 1/2 > or = -1/6 -2/9x
18(1/2 > or = -1/6 -2/9x)[Multiply each term by "18"]
(18)(1/2)>=(18)(-1/6) - (18)(2/9x) [Cancel wherever possible]
9>=-3-4x [Solve for x]
9+3>=-3+3-4x
12>=-4x
12/-4>=-4x/4 [Switch the sign when multiplying or dividing by a negative #]
-3<=x
.
.
3) 2/3x -3 < 1
3(2/3x -3 < 1)[Multiply each term by "3"]
(3)(2/3)x-(3)(3)<(3)(1)
2x-9<3[Solve for x]
2x-9+9<3+9
2x<12
2x/2<12/2
x<6