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Math Help - find solution

  1. #1
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    find solution

    find the step by step solution


    Thanks in advance
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  2. #2
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    Quote Originally Posted by ea12345 View Post
    find the step by step solution


    Thanks in advance
    |2x-7|>3

    Solve this absolute value inequality using the following model:

    If |a|>b, then a<-b \ \ or \ \ a>b

    -----------------------------------------------------------

    -5\leq\frac{4-3x}{2}<1

    Multiply through by 2

    -10\leq4-3x<2

    Subtract 4 throughout the inequality

    -14\leq-3x<-2

    Divide by -3 (don't forget to reverse the inequality signs here)

    Can you finish?
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  3. #3
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    Thanks

    Thanks for reply
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  4. #4
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    Quote Originally Posted by Angel View Post
    |2x-7|>3
    2x-7>+-3 (When we remove the module sign, we put +- both sign for other side)

    so,
    -3<2x-7<3 (Take both -3 and +3, -ve will be less than 2x-7 and +ve will be greater than 2x-7)

    -3<2x-7 , 2x-7<3 (Take saperate -ve and +ve and solve)
    4<2x , 2x<10
    2<x , x<5
    x>2

    2<x<5 required solution (write both answers combinely)
    __________________________________________________ ______________________________
    Thanks,
    Angel
    I must make a correction in your post, Angel. This absolute value inequality is not a conjunction, rather it is a disjunction. Knowing that, we use the following model:

    \boxed{If \ \ |a|>b, \ \ then \ \ a<-b \ \ or \ \ a>b}

    |2x-7|>3 means:

    2x-7<-3 \ \ or \ \ 2x-7>3

    2x<4 \ \ or \ \ 2x>10

    x<4 \ \ or \ \ x>5

    <=======0=======4--------5===========>
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