SOLUTION: I am stuck on a question on one of my tests. . Solve the inequality: |3 - 3x/4| >= 9 . I know the equation will be an inequality, but I've tried several times and I haven't b

Algebra ->  Inequalities -> SOLUTION: I am stuck on a question on one of my tests. . Solve the inequality: |3 - 3x/4| >= 9 . I know the equation will be an inequality, but I've tried several times and I haven't b      Log On


   

Question 731901: I am stuck on a question on one of my tests.
.
Solve the inequality: |3 - 3x/4| >= 9
.
I know the equation will be an inequality, but I've tried several times and I haven't been right. Could I have some help understanding how to tackle this, and all the steps involved?
Found 3 solutions by josgarithmetic, stanbon, Alan3354:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Same as |1-x/4|>=3

Allow for the expression in the absolute value function be positive and negative, and analyze each condition separately.

If 1-x%2F4%3E=0, then abs%281-x%2F4%29=1-x%2F4.
Solve for x in 1-x%2F4%3E=3.

If 1-x%2F4%3C0, then abs%281-x%2F4%29=x%2F4-1.
Solve for x in x%2F4-1%3E=3.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the inequality: |3 - 3x/4| >= 9
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3-(3/4)x >= 9 or 3-(3/4)x <= -9
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-(3/4)x >= 6 or -(3/4)x <= -12
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x <= -8 or x >= 16
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Cheers,
Stan H.
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Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
|3 - 3x/4| >= 9
----------------
3 - 3x/4 >= 9
1 - x/4 >= 3
-x/4 >= 2
-x >= 8
x <= -8
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-(3 - 3x/4) >= 9
3 - 3x/4 <= -9
1 - x/4 <= -3
-x/4 <= - 4
-x <= -16
x >= 16