SOLUTION: 1. 3/2x is greater than or equal to -7/4 {x|x ??} 2. 6x+7<31 {x|x??} 3. 0.4x + 6 is less than or equal to 1.2x-3 {x|x??} 4. 2/3(3x-6)>12 set builder notation to describe t

Question 168342: 1. 3/2x is greater than or equal to -7/4 {x|x ??}
2. 6x+7<31 {x|x??}
3. 0.4x + 6 is less than or equal to 1.2x-3 {x|x??}
4. 2/3(3x-6)>12 set builder notation to describe the complete solution
5. {3,6,9,12} {5,8,10} find intersection
6. -1
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. 3/2x is greater than or equal to -7/4 {x|x ??}
(3/2)x >= (-7/4)
x >= (2/3)(-7/4)
x >= -7/6
{x|x>-7/6}
------------------------
2. 6x+7<31 {x|x??}
6x < 24
x < 4
{x|x<4}
------------------------
3. 0.4x + 6 is less than or equal to 1.2x-3 {x|x??}
0.4x + 6 <= 1.2x-3
0.9x >= 9
x >= 10
{x|x>=10}
-------------------------------
4. 2/3(3x-6)>12 set builder notation to describe the complete solution
(2/3)(3x-6) > 12
2(x-2) > 12
x-2 > 6
x > 8
{x|x>8}
---------------------------------
5. {3,6,9,12} {5,8,10} find intersection
Ans: There are no intersection elements so the answer is "the null set".
--------------------------------
6. -1
===================================
Cheers,
Stan H.

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