Expert: Steve Holleran - 11/7/2007

Question
Hi, I need some help with the questions below. Can you help me with some. The problems are solving the inequality, which is less or greater.

1. 3x < -6
x < -2
x > -2
x > 2
x < 2

2. -5x > 25
x > -5
x < -5
x > 5
x < 5

3. 2x + 6 < -6x - 26
x > -4
x > -5
x < 4
x < -4

4. -4x - 8 < -9x + 24

5. -8x + 2 < 7 + 5(3x - 4)

6. 4 - 6(x + 2) > 5x + 25

7. -5x > -7  

Answer
Hi Janine,

Okay, let's see:

1.  3x < -6  divide both sides by 3:  x < -2

2.  -5x > 25  divide both sides by -5, and remember to reverse the order sign:

     x < -5

3.  2x + 6 < -6x - 26   add 6x to each side:

   8x + 6 < -26      now subtract 6 from each side:

   8x < -32          now divide each side by 8:

    x < -4


4.  -4x - 8 < -9x + 24    add 9x to each side:

   5x - 8 < 24           add 8 to each side:

   5x < 30  divide by 5 :  x < 6

5.  -8x + 2 < 7 + 5(3x-4)  expand the right side:

   -8x + 2 < 7 + 15x - 20  combine on the right:

   -8x + 2 < 15x - 13      subtract 15x from each side:

   - 23x + 2 < -13         subtract 2 from each side:

   -23x < -15  divide by -23; reverse the sign:

      x > 15/23.


6.  4 - 6(x+2) > 5x + 25  expand the left:

   4 - 6x - 12 > 5x + 25 combine on the left:

     - 6x - 8 > 5x + 25  subtract 5x from each side:

    -11x - 8 > 25        add 8 to each side:

    -11x > 33            divide by -11 and reverse:

       x < -3

7.  -5x > -7     just divide each side by -5 and reverse:

     x < 7/5



Good luck!
Steve