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moongazer

  • 4 years ago

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

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  1. moongazer
    • 4 years ago
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    |-6x+10|>7 I already get on how to solve this

  2. hoblos
    • 4 years ago
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    -6x+10 > 7 Or -6x +10 <-7 x<1/2 x>17/6

  3. anonymous
    • 4 years ago
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    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

  4. JamesJ
    • 4 years ago
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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.

  5. moongazer
    • 4 years ago
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    so I can multiply first the -6x+10 by - before applying the rules?

  6. moongazer
    • 4 years ago
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    I am just confused when to change < to this > or vice versa.

  7. JamesJ
    • 4 years ago
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    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)

  8. moongazer
    • 4 years ago
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    if x is negative isn't it I need to change < to >

  9. moongazer
    • 4 years ago
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    This is my only question if x is negative isn't it I need to change < to >

  10. moongazer
    • 4 years ago
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    ???

  11. JamesJ
    • 4 years ago
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    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

  12. moongazer
    • 4 years ago
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    like -6x>-3 to x< 3/6

  13. JamesJ
    • 4 years ago
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    Yes

  14. moongazer
    • 4 years ago
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    because x is negative right ?

  15. moongazer
    • 4 years ago
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    thanks

  16. JamesJ
    • 4 years ago
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    No. It is true that -6x>-3 ==> x< 3/6 because you just multiplied both sides by a negative number, -1/6

  17. JamesJ
    • 4 years ago
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    x itself could be negative or positive or zero.

  18. JamesJ
    • 4 years ago
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    So, have you been able to replicate this solution now: -6x+10 > 7 Or -6x +10 <-7 x<1/2 x>17/6

  19. JamesJ
    • 4 years ago
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    If so, I want to show you one other way to tackle the problem.

  20. moongazer
    • 4 years ago
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    Will the answer be the same if I did 6x-10 > 7 Or 6x -10 <-7 ?? cause I think it will

  21. moongazer
    • 4 years ago
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    yes or no ???

  22. JamesJ
    • 4 years ago
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    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.

  23. JamesJ
    • 4 years ago
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    I'll leave you to it now.

  24. moongazer
    • 4 years ago
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    Thanks!

  25. moongazer
    • 4 years ago
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    :)

  26. moongazer
    • 4 years ago
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    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?

  27. JamesJ
    • 4 years ago
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    yes

  28. moongazer
    • 4 years ago
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    Thank You I just wanted to know. :)

  29. JamesJ
    • 4 years ago
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    ***Correction to post above: In case 2, when -6x+10 < 0, we have | -6x + 10 | > 7 ==> -(-6x+10) > 7 ==> 6x-10 > 7 [NOT -7]

  30. moongazer
    • 4 years ago
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    ok :)

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