anonymous
  • anonymous
Solve the inequality. Give the solution set in interval form. \[frac{ 4 }{ 3 }x - \frac{ 15 }{ 6 } < 3x\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\frac{ 4 }{ 3 }x-\frac{ 15 }{ 6 } < 3x\]
anonymous
  • anonymous
multiply both sides by 6 first to remove annoying fractions
anonymous
  • anonymous
I'm sorry, how exactly do I multiply fractions?

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anonymous
  • anonymous
in this case "multiply" really means cancel, since the whole point of multiplying by 6 is to get rid of the denominators
anonymous
  • anonymous
for example \[6\times \frac{4}{3}x=2\times 4x=8x\]the denominator is now gone
anonymous
  • anonymous
and of course \[-\frac{15}{6}\times 6=-15\]
anonymous
  • anonymous
so the denominator gets canceled and the numerator becomes a whole number by itself?
anonymous
  • anonymous
long and the short of it is you should end up with \[8x-15\leq 18x\]
anonymous
  • anonymous
yes
anonymous
  • anonymous
since the least common multiply of 6 and 3 is 6, if you multiply both sides by 6 there will be no denominators left
anonymous
  • anonymous
I'm a little confused...I thought the lcm was 3...can you explain that to me? I haven't been in a math class for the last two years so my knowledge on the basics are really weak right now
anonymous
  • anonymous
do I cancel the denominator out in the other fraction as well?
anonymous
  • anonymous
yes you want to get rid of both denominators 3 and 6
anonymous
  • anonymous
btw the least common multiple is not the greatest common factor for example the least common multiply of 4 and 6 is 12 their greatest common factor is 2
anonymous
  • anonymous
so if for example you had \[\frac{1}{4}x-\frac{5}{6}<3\]you would multiply both sides by 12 go get\[3x-10<36\]
anonymous
  • anonymous
I'm sooooo confused >.< I understand that you're multiplying both denominators by the LCM now but I don't see how you got 3x-10<30 ... i tried to understand how you got the answer for the first one as well but it isn't computing with me...is there any other way to explain it? I'm sorry..my comprehension is a little slow

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