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Question 1119764: Hi, I need some help understanding this absolute value inequality function. I don't understand why the answer says 'x' is not a real number.
"-5|x-3|-5<15".
I worked it out and I thought the solution was x<-1 or x>7 but it wasn't correct according to the answer. Could you please help me? Thank you!
Found 3 solutions by ikleyn, josgarithmetic, MathTherapy:
Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website! .
-5|x-3|-5 < 15.
Add 5 to both sides of this inequality. You will get an EQUIVALENT inequality
-5|x-3| < 20.
Divide by (-5) both sides of the last inequality. You will get an EQUIVALENT inequality
|x-3| > -4. (Notice the inequality sign changed its direction !)
Since the absolute value function is non-negative for any of its argument, the solution set for the last inequality
is the set of ALL REAL NUMBERS.
Plot y = -5|x-3|-5 (red) and y = 15 (green)
Solved.
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Be aware: The solution and the answer by @josgarithmetic "  " is T O T A L L Y W R O N G,
so for your safety simply ignore it.
This person does not know basics.
Answer by josgarithmetic(39617)  (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Hi, I need some help understanding this absolute value inequality function. I don't understand why the answer says 'x' is not a real number.
"-5|x-3|-5<15".
I worked it out and I thought the solution was x<-1 or x>7 but it wasn't correct according to the answer. Could you please help me? Thank you!
The left side as it is WILL ALWAYS BE NEGATIVE (< 0), and ANY negative number will obviously be LESS THAN a POSITIVE number, as the right side is.
If the - 5 is added to both sides, and both sides are then divided by - 5, we'd get a POSITIVE NUMBER on the left side being GREATER THAN the resulting
NEGATIVE number on the right, which is ALWAYS TRUE.
Any which way you take it, the solution is the set of ALL REAL NUMBERS.
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