SOLUTION: Can you please Help me with this problem: Fine the soulution set for the inequality. -15x + 21 <(absolute value) -3(4x + 1)

Question 515065: Can you please Help me with this problem: Fine the soulution set for the inequality.
-15x + 21 <(absolute value) -3(4x + 1)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Fine the soulution set for the inequality.
-15x + 21 <(absolute value) -3(4x + 1)
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-15x + 21 < |-3(4x+1)|
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Note: The -3(4x+1) could be positive, zero, or it could be negative.
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It is positive if (4x+1)<0 , i.e. x < -1/4
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Draw a Number line and plot x = -1/4,
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Now, if x < -1/4, the equation becomes
-15x + 21 < -3(4x+1)
-15x + 21 < -12x-3
21 < 3x-3
3x > 24
x > 8
But those x's are not < -1/4.
So there are no solutions below x = -1/4,
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But, if x >= -1/4, the equation becomes
-15x+21 < 3(4x+1)
-15x +21 < 12x + 3
27x > 18
x > 2/3
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Solutions: x > 2/3
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Cheers,
Stan H.

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