|-6x+10|>7 show your solutions please.

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|-6x+10|>7 show your solutions please.

Mathematics
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|-6x+10|>7 I already get on how to solve this
-6x+10 > 7 Or -6x +10 <-7 x<1/2 x>17/6
Well moongazer whenever an expression is inside a mod function then you have to consider two cases either positive or negative that is what hobolos replied

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Whenever you have an equation | stuff | > c, then you need to consider two cases. 1. If stuff > 0, then by definition of absolute value | stuff | = stuff and therefore | stuff | > c => stuff > c This is now an ordinary algebra inequality that you can solve. That is the first case you have here: -6x + 10 > 7 2. There if of course a second case: stuff < 0. In which case, by definition of absolute value | stuff | = - stuff and therefore | stuff | > c => -stuff > c. That is the second case you have here -(-6x+10) > 7 Now take these two cases and solve them. That's the algebraic approach.
so I can multiply first the -6x+10 by - before applying the rules?
I am just confused when to change < to this > or vice versa.
By definition if y < 0, then |y| = -y. For example, if y = -3, then |y| = |-3| = 3 = -y. Write here y = -6x + 10. If y = -6x + 10 < 0, then |y| = |-6x + 10| = -(-6x+10)
if x is negative isn't it I need to change < to >
This is my only question if x is negative isn't it I need to change < to >
???
Whenever you have an inequality a < b if you multiply both sides by a negative number then the inequality changes. For instance a < b ==> -2a > -2b a < b ==> -17a > -17b a < b ==> -a > -b
like -6x>-3 to x< 3/6
Yes
because x is negative right ?
thanks
No. It is true that -6x>-3 ==> x< 3/6 because you just multiplied both sides by a negative number, -1/6
x itself could be negative or positive or zero.
So, have you been able to replicate this solution now: -6x+10 > 7 Or -6x +10 <-7 x<1/2 x>17/6
If so, I want to show you one other way to tackle the problem.
Will the answer be the same if I did 6x-10 > 7 Or 6x -10 <-7 ?? cause I think it will
yes or no ???
In case 1, when -6x + 10 > 0, we have | -6x + 10 | > 7 ==> (-6x+10) > 7 ==> 6x-10 < -7 In case 2, when -6x+10 < 0, we have | -6x + 10 | > 7 ==> -(-6x+10) > 7 ==> 6x-10 > -7 So the answer to your question is yes. But it's very important to understand why. If you just blindly try to use rules for problem solving without understanding how they relate the definition and properties of the mathematics objects you're using, you're certain to get into trouble sooner or later.
I'll leave you to it now.
Thanks!
:)
I have another question in an ordinary equality or inequality if I multiplied the left side by negative; do I also need to multiply the right side by negative?
yes
Thank You I just wanted to know. :)
***Correction to post above: In case 2, when -6x+10 < 0, we have | -6x + 10 | > 7 ==> -(-6x+10) > 7 ==> 6x-10 > 7 [NOT -7]
ok :)

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