Thank you for the opportunity to help you with your question!

#22) Split into two (4x <16; 12x > 144)

4x <16 divide both sides by 4; x <4

12x > 144 divide both sides by 12; x >12

#24) Do the same as #22

8x < -32 divide both sides by 8

-6x </- 48 divide both side by -6

#28) the max the rod can be in length is 4.6 + .02 = 4.52; the shortest 4.48

the machinist must reduce it by .08cm; least amount to reduce 4.78 - 4.52 = .26cm; max to reduce 4.78 - 4.48 = .30cm

The machinist should reduce the rod between .26cm and .30 cm to make it within +/- .02cm.

Because of the time limit to answer questions, I will answer the remaining questions in the follow up. Please give me a couple of minutes to do so. Thank you for your understanding!

Please let me know if you need any clarification. I'm always happy to answer your questions.

Sep 17th, 2015

#32) expand; 3/5x - 36/5 > x -24

multiply both sides by 5; 3x - 36 > (x - 24) 5

expand (x -24) 5; 5x -120

3x - 36 > 5x -120; add 36 to both sides and then subtract 5x from both sides

-2x > -84; multiply both sides by -1 (to reverse inequality)

2x > 84; divide both sides by 2

x < 42

Sep 17th, 2015

#36)

BC=4 and AC=8 - AB

AB < BC + AC (since any side is less than the sum of the other 2 sides)

AB < 4 + 8 - AB (since BC = 4, and AC = 8 - AB)

AB < 12 - AB

Moving AB to the left side

2AB < 12

AB < 6 (therefore the side has to be less than 6).