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anonymous

  • one year ago

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

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  1. anonymous
    • one year ago
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    \[\frac{ 4 }{ 3 }x-\frac{ 15 }{ 6 } < 3x\]

  2. anonymous
    • one year ago
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    multiply both sides by 6 first to remove annoying fractions

  3. anonymous
    • one year ago
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    I'm sorry, how exactly do I multiply fractions?

  4. anonymous
    • one year ago
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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

  5. anonymous
    • one year ago
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    for example \[6\times \frac{4}{3}x=2\times 4x=8x\]the denominator is now gone

  6. anonymous
    • one year ago
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    and of course \[-\frac{15}{6}\times 6=-15\]

  7. anonymous
    • one year ago
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    so the denominator gets canceled and the numerator becomes a whole number by itself?

  8. anonymous
    • one year ago
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    long and the short of it is you should end up with \[8x-15\leq 18x\]

  9. anonymous
    • one year ago
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    yes

  10. anonymous
    • one year ago
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    since the least common multiply of 6 and 3 is 6, if you multiply both sides by 6 there will be no denominators left

  11. anonymous
    • one year ago
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    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

  12. anonymous
    • one year ago
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    do I cancel the denominator out in the other fraction as well?

  13. anonymous
    • one year ago
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    yes you want to get rid of both denominators 3 and 6

  14. anonymous
    • one year ago
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    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

  15. anonymous
    • one year ago
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    so if for example you had \[\frac{1}{4}x-\frac{5}{6}<3\]you would multiply both sides by 12 go get\[3x-10<36\]

  16. anonymous
    • one year ago
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    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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