Solve the inequality. Give the solution set in interval form. \[frac{ 4 }{ 3 }x - \frac{ 15 }{ 6 } < 3x\]

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Solve the inequality. Give the solution set in interval form. \[frac{ 4 }{ 3 }x - \frac{ 15 }{ 6 } < 3x\]

Mathematics
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\[\frac{ 4 }{ 3 }x-\frac{ 15 }{ 6 } < 3x\]
multiply both sides by 6 first to remove annoying fractions
I'm sorry, how exactly do I multiply fractions?

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in this case "multiply" really means cancel, since the whole point of multiplying by 6 is to get rid of the denominators
for example \[6\times \frac{4}{3}x=2\times 4x=8x\]the denominator is now gone
and of course \[-\frac{15}{6}\times 6=-15\]
so the denominator gets canceled and the numerator becomes a whole number by itself?
long and the short of it is you should end up with \[8x-15\leq 18x\]
yes
since the least common multiply of 6 and 3 is 6, if you multiply both sides by 6 there will be no denominators left
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
do I cancel the denominator out in the other fraction as well?
yes you want to get rid of both denominators 3 and 6
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
so if for example you had \[\frac{1}{4}x-\frac{5}{6}<3\]you would multiply both sides by 12 go get\[3x-10<36\]
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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