SOLUTION: Please Solve the inequality 7x-9>=x+3 where 7x-9 is an absolute value and in bars and it is greater then equals to x+3

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Question 972800: Please Solve the inequality 7x-9>=x+3
where 7x-9 is an absolute value and in bars and it is greater then equals to x+3
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
abs%287x-9%29%3E=abs%28x%2B3%29

To be easy, either the signs of each argument are same or they are opposite. Examining the simple cases would be better for understanding, but avoiding here.

You want both of these to be true for a solution.
7x-9%3E=x%2B3 AND 7x-9%3E=-x-3

-
-
6x-12%3E=0
x-2%3E=0
x%3E=2

8x-6%3E=0
8x%3E=6
4x%3E=3
x%3E=3%2F4

The first condition makes x%3E=2; and the second condition makes x%3E=3%2F4. We can check intervals around the critical x values just to be more certain.

Between the two:
abs%287x-9%29%3E=abs%28x%2B3%29
pick 1.
abs%287%2A1-9%29%3E=abs%281%2B3%29
abs%28-2%29%3E=abs%284%29
2%3E=4, FALSE.

Left of 3/4:
pick 0.
abs%287%2A0-9%29%3E=abs%280%2B3%29
abs%28-9%29%3E=abs%283%29
9%3E=3, TRUE.

Greater than 2:
pick 3.
abs%287%2A3-9%29%3E=abs%283%2B3%29
12%3E=6, TRUE.

Actual answer is highlight%28x%3E=3%2F4%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Please Solve the inequality 7x-9>=x+3
where 7x-9 is an absolute value and in bars and it is greater then equals to x+3
abs%287x+-+9%29+%3E=+x+%2B+3 results in: highlight_green%28system%28x+%3C=+%283%2F4%29_or%2Cx+%3E=+2%29%29