SOLUTION: please solve this inequalitys step by step 1. (-9m)+(-m)+(-7) >= 43 2. 5x+8< 9x+24 3. 1/2(-4x -8) > 1/4(16x+24)

Algebra ->  Inequalities -> SOLUTION: please solve this inequalitys step by step 1. (-9m)+(-m)+(-7) >= 43 2. 5x+8< 9x+24 3. 1/2(-4x -8) > 1/4(16x+24)       Log On


   

Question 161392: please solve this inequalitys step by step
1. (-9m)+(-m)+(-7) >= 43
2. 5x+8< 9x+24
3. 1/2(-4x -8) > 1/4(16x+24)
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
1. (-9m)+(-m)+(-7) >= 43
-9M-M-7>=43
-10M>=43+7
-10M>=50
M<=50/-10 THE > SIGN CHANGES TO A < SIGN WHEN DIIVIDING BY A NEGATIVE VALUE.
M<=-5 ANSWER.
PROOF:
LET M=-6
-9(-6)-(-6)-7>=43
54+6-7>=43
60-7>=43
53>=43
-------------------------------------------------
2. 5x+8< 9x+24
5X-9X<24-8
-4X<16
X>16/-4 AGAIN DIVIDING BY A NEGATIVE VALUR CHANGES THE < SIGN TO A > SIGN.
X>-4 ANSWER.
PROOF:
LET X=-3
5(-3)+8<9(-3)+24
-15+8<-27+24
-7<-3
-------------------------------------------------
3. 1/2(-4x -8) > 1/4(16x+24)
-4X/2-8/2>16X/4+24/4
-2X-4>4X+6
-2X-4X>6+4
-6X>10
X<10/-6 AGAIN A SIGN CHNGE.
X<-5/3 ANSWER.
PROOF:
LET X=-6/3=-2
1/2(-4*-2-8)>1/4(16*-2+24)
1/2(8-8)>1/4(-32+24)
0>1/4*-8
0>-2