Verified Answer :

  1. 6x-4< -34, or 3x+10 > 10. 

    6x-4 < -34. 
    6x < -34 + 4 
    6x < -30 
    X < -5. 

    3x + 10 > 10. 
    3x > 10 - 10 
    3x > 0 
    X > 0. 

    2. -2 <= 2x-4 < 4. 
    Add 4 to each end and the center: 
    -2 + 4<= 2x-4+4 < 4+4. 
    2 <= 2x < 8 
    Divide each end and center by 2: 
    1 <= X < 4. 

    The compound inequality is actually 2 
    inequalities and can be solved separately: 

    2x-4 => -2, and 2x-4 < 4. 

    2x-4 => -2. 
    2x => -2+4 
    2x=> 2 
    X => 1. 

    2x-4 < 4. 
    2x < 4+4 
    2x < 8 
    X < 4. 

    Solution: 1< = X < 4. or X => 1, and X<4 

     TO CHECK: 

    1. Substitute any number < -5 for X. 
    Eq2: Subst. any number > 0 for X.

Related Questions