jewlzme17 one year ago Find the value x such that f(x)=0, if f(x)=(3x-4)/(5)

1. random231

just solve (3x-4)/5=0

2. anonymous

$$\bf f(x)={\color{blue}{ y}}=0\qquad {\color{blue}{ f(x)}}=\cfrac{3x-4}{5}\qquad thus \\ \quad \\ {\color{blue}{ 0}}=\cfrac{3x-4}{5}\impliedby \textit{solve for "x"}$$

3. jewlzme17

I already know all of that I just don't remember how to solve (3x-4)/5

4. freckles

(3x-4)/5 there is nothing to solve here do you mean you don't remember how to solve (3x-4)/5=0?

5. freckles

the fraction is zero when the top is 0

6. freckles

that you only have to solve 3x-4=0

7. jewlzme17

so the zero cancels out the 5?

8. dinamix

(3x-4)=0 *5 3x=4 x=

9. dinamix

@jewlzme17 u should try little

10. jewlzme17

I know the answer it 4/3 its just I am having trouble understanding how. You guys are all saying different things and it's confusing. Like can someone just break it down barney style without being rude?

11. freckles

if 3x-4=0 then 3x has to be 4 another way to say this is 3x=4

12. freckles

can you solve for x now?

13. freckles

no one has said anything different

14. freckles

each of us has given you part of how to get there

15. freckles

@jdoe0001 showed you exactly what f(x)=0 meant @dinamix showed you how to get to 3x=4

16. freckles

oh and i forgot to add what I said @freckles said f(x)=0 when the numerator=0

17. jewlzme17

What I'm confused on is what you do with the denominator?

18. freckles

the bottom is always 5 it has no deciding factor when the fraction is 0

19. freckles

do you know that 0/anything is 0 (when anything isn't 0)

20. freckles

$h(x)=\frac{f(x)}{g(x)}=0 \text{ when } f(x)=0 \text{ when } x \text{ is in the domain of } h$

21. freckles

the only that gets to decide a fraction is 0 when the top is 0 on that function's domain of course

22. jewlzme17

OKay that makes so much more sense. Thank you

23. freckles

$\frac{3x-4}{5}=0 \implies 3x-4=0$

24. freckles

though you could have also decide to multiply both sides by 5 and that also works