SOLUTION: What is |7x+4| > 74 and 7x+4 < -74

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Question 1001424: What is |7x+4| > 74 and 7x+4 < -74
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
The first is an absolute value inequality, and the second is an inequality.

THE INEQUALITY
7x%2B4%3C-74
7x%3C-74-4
7x%3C-78
x%3C-78%2F7



THE ABSOLUTE VALUE INEQUAL
If 7x+4 positive,
7x%2B4%3E74
Solve this.
If 7x+4 negative,
-7x-4%3E74
Solve this.
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Two separate solutions, and you must find the part or parts which makes the original absolute inequality true. Find what makes BOTH conditions true, because this requires the conjunction AND.

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What or how did not make sense to you?
Two given mathematical inequalities were given. One is an absolute value inequality, and the other is just an inequality.

The absolute value inequality needs you to check the two separate cases of 7x+4 nonnegative, and 7x+4 negative. The solution to the original statement is the parts of the separate solutions which make BOTH conditions true.

The regular inequality just needs you to use the typical inverse operations (number properties, properties of inequality) to isolate x; most of the properties work the same way as do for equalities.