## anonymous one year ago Solve the inequality. Give the solution set in interval form. $frac{ 4 }{ 3 }x - \frac{ 15 }{ 6 } < 3x$

1. anonymous

$\frac{ 4 }{ 3 }x-\frac{ 15 }{ 6 } < 3x$

2. anonymous

multiply both sides by 6 first to remove annoying fractions

3. anonymous

I'm sorry, how exactly do I multiply fractions?

4. anonymous

in this case "multiply" really means cancel, since the whole point of multiplying by 6 is to get rid of the denominators

5. anonymous

for example $6\times \frac{4}{3}x=2\times 4x=8x$the denominator is now gone

6. anonymous

and of course $-\frac{15}{6}\times 6=-15$

7. anonymous

so the denominator gets canceled and the numerator becomes a whole number by itself?

8. anonymous

long and the short of it is you should end up with $8x-15\leq 18x$

9. anonymous

yes

10. 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

11. 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

12. anonymous

do I cancel the denominator out in the other fraction as well?

13. anonymous

yes you want to get rid of both denominators 3 and 6

14. 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

15. anonymous

so if for example you had $\frac{1}{4}x-\frac{5}{6}<3$you would multiply both sides by 12 go get$3x-10<36$

16. 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