iosangel:
can someone walk me through this I don't understand this equation at all
iosangel:
3/x+5=8/x+2
Hero:
Is it ONE: \(\dfrac{3}{x} + 5 = \dfrac{8}{x} + 2\) or TWO: \(\dfrac{3}{x + 5} = \dfrac{8}{x + 2}\)?
iosangel:
two
Hero:
Okay, so going forward, next time you have an equation like that write it this way using parentheses: 3/(x + 5) = 8/(x + 2)
iosangel:
ok
Hero:
Anyways, to solve it, you have to do what is called cross multiplication. Anytime you have two ratios equated to each other: \(\dfrac{a}{b} = \dfrac{c}{d}\) you cross multiply to get \(ad = bc\)
Hero:
In this case you would cross multiply to get \(3(x + 2) = 8(x + 5)\) Are you able to solve for \(x\) from here?
iosangel:
No
Hero:
Do you know how to apply the distributive property here? \(a(b + c) = ab + ac\)
iosangel:
yes
Hero:
Okay, try doing that on both sides. Let me know what you get.
Hero:
We have a drawing tool btw just in case you didn't know: |dw:1567613363451:dw|
iosangel:
3*x=3x 3*2=6 8*x=8x 8*5=40 3x+6=8x+40
iosangel:
Im not sure if that right
Hero:
Did you apply the distributive property to 3(x + 5) = 8(x + 2)? I think you applied the distributive property incorrectly. You should write it linearly.
iosangel:
I got 3x+6=8x+40
Hero:
Sorry that's not right. You multiplied the wrong numbers you need to start over from here but write horizontally. 3(x + 5) = 8(x + 2)
iosangel:
what i know is that i multiply 3 *x then 3*5 right?
Hero:
Correct
iosangel:
Then i gtt 3x+15
Hero:
And what do you get for the other expression?
iosangel:
8x+16
Hero:
Very good. Now continue solving for x
iosangel:
3x+15=8x+16 8x-3x+15=8x+16-8x 5x+15=16 Like this?
Hero:
Looks right. Continue solving for x
Hero:
Hang on a minute. What have you done?
Hero:
Somehow you've managed to mix things up again.
Hero:
You need to subtract the same thing from both sides per line.
iosangel:
ok for 8x+16-8x ive crossed out the 8x and left me with 16 and 8x-3x+1 i solved and got 5x+15
Hero:
You'll need to start over again from 3x + 15 = 8x + 16
iosangel:
ok
Hero:
You have to subtract the same thing from both sides PER LINE. You cannot subtract 3x on one side then 8x on the other side.
iosangel:
here i subtract 8x from both sides right?
Hero:
You have to subtract 3x on BOTH sides
iosangel:
ok
iosangel:
but why not 8x?
iosangel:
will that be for later?
Hero:
Let's do one thing at a time. Subtract 3x on both sides. Then we'll go from there.
iosangel:
ok 3x + 15-3x = 8x + 16-3x 3x will be crossed out and leaves with 15 then 8x+16-3x=5x+16= so i got `15=5x+16
Hero:
And what are you going to do next?
iosangel:
subtract 16?
iosangel:
from both sides
Hero:
Exactly
iosangel:
ok 15-16=5x+16-16 -1=5x
Hero:
There's only one step left. Do you know what it is?
iosangel:
divide
Hero:
Divide what?
iosangel:
divide 5
iosangel:
both sides
iosangel:
then i gotx= -1/5
Hero:
Correct.
iosangel:
Ok thank you
Hero:
Now you have to check it
iosangel:
oh
iosangel:
idk how to do that tbh
Hero:
Plug the -1/5 back into the x of the original equation then evaluate both sides.
iosangel:
to both x?
Hero:
Correct
Hero:
If it is correct you should end up with the same value on both sides.
iosangel:
ok
iosangel:
3/(-1/5+5) =8/(-1/5+2)
iosangel:
Lol i got it wrong
Hero:
How do you figure?
iosangel:
i think it was 34/5
Hero:
What are you referring to?
iosangel:
i was supposed to multiply x+5 from both sides instead of doing distributive property thing im not sure.
Hero:
Can you post a screenshot of the original problem?
iosangel:
Ok
Hero:
Like from the book
iosangel:
It was a practice problem from a recording from my teacher
iosangel:
Ill show you how she wrote it
iosangel:
|dw:1567616162779:dw|
Hero:
That's not what you wrote originally
Hero:
Ah I see. I'm the one who made the mistake.
Hero:
It was 3(x + 2) = 8(x + 5)
Hero:
What matters though is knowing how to do the steps.
iosangel:
yes
Hero:
Consider what we did as an example
iosangel:
ok
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