SOLUTION: Solve |4-5x| ≤ 9. Solve |3x+1| > 8.

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Question 1186195: Solve |4-5x| ≤ 9.
Solve |3x+1| > 8.

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
matrix%281%2C3%2Cabs%284-5x%29%2C%22%22%3C=%22%22%2C9%29

Rewrite without absolute values:

matrix%281%2C5%2C-9%2C%22%22%3C=%22%22%2C4-5x%2C%22%22%3C=%22%22%2C9%29

Solve for x in the middle:

Add -4 to all three sides:

matrix%281%2C5%2C-9-4%2C%22%22%3C=%22%22%2C4-5x-4%2C%22%22%3C=%22%22%2C9-4%29

matrix%281%2C5%2C-13%2C%22%22%3C=%22%22%2C-5x%2C%22%22%3C=%22%22%2C5%29

Divide through by -5, which reverse the inequalities:



matrix%281%2C5%2C13%2F5%2C%22%22%3E=%22%22%2Cx%2C%22%22%3E=%22%22%2C-1%29

Rewrite the inequality using ≤

matrix%281%2C5%2C-1%2C%22%22%3C=%22%22%2Cx%2C%22%22%3C=%22%22%2C13%2F5%29

In interval notation, that is written:

matrix%281%2C5%2C+%22%5B%22%2C+-1%2C+%22%2C%22+%2C+13%2F5%2C%22%5D%22%29

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

matrix%281%2C3%2Cabs%283x%2B1%29%2C%22%22%3E%22%22%2C8%29

Rewrite without absolute values:



Solve each part for x.  Add -1 to all sides





Divide all sides by 3





In interval notation that's:

%28matrix%281%2C3%2C-infinity%5E%22%22%2C%22%2C%22%2C-3%5E%22%22%29%29U%28matrix%281%2C3%2C7%2F3%2C%22%2C%22%2Cinfinity%29%29

Edwin