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#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!
#32) expand; 3/5x - 36/5 > x -24
multiply both sides by 5; 3x - 36 > (x - 24) 5
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
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).
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