Results 1 to 4 of 4

Thread: Absolute Value Inequality

  1. #1
    Banned
    Joined
    Oct 2007
    Posts
    158

    Absolute Value Inequality

    solve the inequality

    $\displaystyle \left| 5x+4\right| >6$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,854
    Thanks
    138
    Quote Originally Posted by OzzMan View Post
    solve the inequality

    $\displaystyle \left| 5x+4\right| >6$
    $\displaystyle |5x+4| = \left\{\begin{array}{lcr}5x+4 &if& x\geq -\frac45\\ -(5x+4)&if &x < -\frac45\end{array}\right.$

    That means you have 2 inequalities:

    $\displaystyle \begin{array}{lcr}5x+4>6 &if& x\geq -\frac45\\ -(5x+4)>6&if &x < -\frac45\end{array}$

    $\displaystyle \begin{array}{lcr}x> \frac25 &if& x\geq -\frac45\\ x<-2&if &x < -\frac45\end{array}$

    The solution of this inequality is: $\displaystyle x < -2~\vee~x > \frac25$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Oct 2007
    Posts
    158
    I see my error. Thanks. Just one question though. How come you wrote $\displaystyle 5x+4\quad if\quad x\ge -\frac{4}{5}\quad instead\; of\quad x>-\frac{4}{5}$
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,854
    Thanks
    138
    Quote Originally Posted by OzzMan View Post
    I see my error. Thanks. Just one question though. How come you wrote $\displaystyle 5x+4\quad if\quad x\ge -\frac{4}{5}\quad instead\; of\quad x>-\frac{4}{5}$
    The definiton of an absolute value is:

    $\displaystyle |x| = \left\{\begin{array}{lcr}x & if & x \geq 0\\-(x) & if & x <0 \end{array}\right.$

    I only tried to use the definition correctly
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Sep 7th 2011, 08:11 AM
  2. Absolute Value Inequality
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 4th 2011, 10:43 PM
  3. Absolute value Inequality
    Posted in the Pre-Calculus Forum
    Replies: 7
    Last Post: Mar 9th 2011, 01:36 PM
  4. Absolute value inequality
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: Sep 19th 2009, 04:45 PM
  5. Absolute Value Inequality Help
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Jan 12th 2009, 01:27 AM

Search Tags


/mathhelpforum @mathhelpforum