Question 215617: 4X+7<5X-2<8X
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! 4x +7<5x-2<8x,,,,add 2 to each term
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4x +7 +2 < 5x-2+2 < 8x +2
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4x +9<5x<8x+2,,,,,divide by 5
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(4x+9)/5 < 1x < (8x+2)/5,,,,,
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or,,,,.8x +1.8<1x<1.6x +.4,,,,
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solving using two problems,,,.8x +1.8<1x,,,subtract .8x
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1.8<.2x,,,,divide by .2
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9<1x,,,,,answer
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or 1x<1.6x +.4,,,,,subtract 1.6x
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-.6x < .4,,,,,,,divide by (-.6) and flip sign
.,,,,1x>-.667,,,,,,,answer
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check,,,,,,,a,,,,-.667,,,,,b,,,,9,,,,,c
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a, Let x= -1,,,,,,4(-1)+7<5(-1)-2<8(-1)
,,,,,,,,,-4 +7 <-5<-8
,,,,,,,,3 <-5<-8,,,,,,not true
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b,,,,let x= 0,,,,,7<-2<0,,,,,not true
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c,,,,,let x =10,,,,4(10)+7<5(10)-2<8(10)
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,,,,,,,,,,,,,,47<48<80,,,,,,,ok
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Therefore answer is 1x >9
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