moongazer
  • moongazer
|-6x+10|>7 show your solutions please.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
moongazer
  • moongazer
|-6x+10|>7 I already get on how to solve this
hoblos
  • hoblos
-6x+10 > 7 Or -6x +10 <-7 x<1/2 x>17/6
anonymous
  • anonymous
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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JamesJ
  • JamesJ
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.
moongazer
  • moongazer
so I can multiply first the -6x+10 by - before applying the rules?
moongazer
  • moongazer
I am just confused when to change < to this > or vice versa.
JamesJ
  • JamesJ
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)
moongazer
  • moongazer
if x is negative isn't it I need to change < to >
moongazer
  • moongazer
This is my only question if x is negative isn't it I need to change < to >
moongazer
  • moongazer
???
JamesJ
  • JamesJ
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
moongazer
  • moongazer
like -6x>-3 to x< 3/6
JamesJ
  • JamesJ
Yes
moongazer
  • moongazer
because x is negative right ?
moongazer
  • moongazer
thanks
JamesJ
  • JamesJ
No. It is true that -6x>-3 ==> x< 3/6 because you just multiplied both sides by a negative number, -1/6
JamesJ
  • JamesJ
x itself could be negative or positive or zero.
JamesJ
  • JamesJ
So, have you been able to replicate this solution now: -6x+10 > 7 Or -6x +10 <-7 x<1/2 x>17/6
JamesJ
  • JamesJ
If so, I want to show you one other way to tackle the problem.
moongazer
  • moongazer
Will the answer be the same if I did 6x-10 > 7 Or 6x -10 <-7 ?? cause I think it will
moongazer
  • moongazer
yes or no ???
JamesJ
  • JamesJ
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.
JamesJ
  • JamesJ
I'll leave you to it now.
moongazer
  • moongazer
Thanks!
moongazer
  • moongazer
:)
moongazer
  • moongazer
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?
JamesJ
  • JamesJ
yes
moongazer
  • moongazer
Thank You I just wanted to know. :)
JamesJ
  • JamesJ
***Correction to post above: In case 2, when -6x+10 < 0, we have | -6x + 10 | > 7 ==> -(-6x+10) > 7 ==> 6x-10 > 7 [NOT -7]
moongazer
  • moongazer
ok :)

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