How would I solve 1/2-2/3x=1/4?

Question

shadowlegendx · Answer

$$\frac{ 1 }{ 2 } - \frac{ 2 }{ 3 } x = \frac{ 1 }{ 4 }$$

shadowlegendx · Answer

Is this what it looks like

walgenbajr12 · Answer

yes

shadowlegendx · Answer

Do you know what the first step is?

walgenbajr12 · Answer

I made the common factor 12 and multipled throughout

shadowlegendx · Answer

What did you get?

walgenbajr12 · Answer

12-24+12x=12

shadowlegendx · Answer

no no no

shadowlegendx · Answer

$$12(\frac{ 1 }{ 2 } - \frac{ 2 }{ 3 } x = \frac{ 1 }{ 4 })$$

shadowlegendx · Answer

We get:

shadowlegendx · Answer

$$\frac{ 12 }{ 2 } - \frac{ 24 }{ 3 }x = \frac{ 12 }{ 4 }$$

shadowlegendx · Answer

Do you understand how I got those numbers?

walgenbajr12 · Answer

Yeah but I thought that because the bottom all has the common factor of 12 they become canceled out

shadowlegendx · Answer

They do, but not in the way you're thinking

otherworldly · Answer

why don't u just d this 
1/2 - 1/4 = 2/3x and go from there

walgenbajr12 · Answer

okay!

shadowlegendx · Answer

Remember

$$12 = \frac{ 12 }{ 1 }$$

Just multiply across

shadowlegendx · Answer

@OtherWorldly He should understand it this way first

otherworldly · Answer

ok

walgenbajr12 · Answer

so now what do I do?

shadowlegendx · Answer

Going back to what I have way up there, we continue

$$6 - 8x = 3$$

shadowlegendx · Answer

We got that from this

$$\frac{ 12 }{ 2 } - \frac{ 24 }{ 3 }x = \frac{ 12 }{ 4 }$$

walgenbajr12 · Answer

how???

otherworldly · Answer

divided

shadowlegendx · Answer

What part do you not understand?

walgenbajr12 · Answer

oh okay got it!!

shadowlegendx · Answer

Alright we continue

$$6 - 8x = 3$$

$$-8x = -3$$

walgenbajr12 · Answer

so it would just be 3/8/

shadowlegendx · Answer

Correct

shadowlegendx · Answer

$$x = \frac{ -3 }{ -8 }$$

walgenbajr12 · Answer

Thank you so much!! Can you help me with one more problem??

shadowlegendx · Answer

Simplified 

$$x = \frac{ 3 }{ 8 }$$

shadowlegendx · Answer

Sure

walgenbajr12 · Answer

-4/7b + 7=11

I have a bunch like this I just need to remember how to solve one of them so I can work on the rest. I forgot how to solve for b if theres a fraction. I tried taking 7-11 which equals -4 and tried dividing -4 by -4/7 to get B but my online homework checker says its wrong

shadowlegendx · Answer

Does it look like this?

$$\frac{ -4}{ 7 }b + 7 = 11$$

walgenbajr12 · Answer

correct

shadowlegendx · Answer

$$7(\frac{ -4 }{ 7 } +7 = 11)$$

shadowlegendx · Answer

$$-4b + 49 = 77$$

shadowlegendx · Answer

$$-4b = 28$$

shadowlegendx · Answer

$$b = -7$$

walgenbajr12 · Answer

why did you multiply by 7

shadowlegendx · Answer

Let me rewrite that one step, I forgot the b.

$$7(\frac{ -4 }{ 7 }b + 7 = 11)$$

shadowlegendx · Answer

To eliminate the fraction

walgenbajr12 · Answer

ohhhh okay! Thank you so so much! You were a really big help. I was starting to get really frustrated with myself!

shadowlegendx · Answer

tbh I did it the hard way. You could subtract 7 first, from 11. 

-4/7b = 4

Multiply by 7

-4b = 28

b = -7

shadowlegendx · Answer

Same result

shadowlegendx · Answer

I personally like to do it the harder way to keep my mind doing harder calculations

shadowlegendx · Answer

But do it either way

otherworldly · Answer

i was wondering y u were doing it the hard way XD

shadowlegendx · Answer

I knew you were :P

shadowlegendx · Answer

I have class, I'll be back online later today if you need further help. Have a nice day guys, hope you get your work done ^-^

otherworldly · Answer

k good luck in class bye