Question

What are the solutions for x in the proportion x plus 6 all over 2 times x equals x over 2?

Answer 1

is it?
\(\huge {x+6 \over 2x } = { x \over 2} \)

Answer 2

yes :))

Answer 3

ok so we cross multiply meaninggg:
\( (x+6)(2)=(2x)(x)
Now we would have to distribute

Answer 4

um so it would be 2x+2=2x^2?

Answer 5

yes it would be 2x+12=2x^2

Answer 6

Yes but then we need to bring over everything to one side
\( 2x^2-2x+12 =0 \)

Answer 7

okkkk

Answer 8

Its a parabola. Do you know what to do from here?

Answer 9

um no how do you get two solutions for x if they are on the same side?

Answer 10

ok ill just give u the steps
First you factor all that you can.
In this particular equation we can factor out a 2
\( 2(x^2-x+6) \)

Answer 11

next we use that quadratic factoring
We find two numbers that when you add them they equal -1 and when you multiply then it equals 6. So what do u think the 2 numbers are?

Answer 12

-3 and 2?

Answer 13

yaaaaaaaaaaaaaaaaa

Answer 14

thankkkk youu soo much!! can you help me with 1 more pleasee??? :)

Answer 15

so now we replace the -x with 2x-3x which is in essence -x
\( 2( x^2+2x-3x-6)=0 \)
\( 2((x^2+2x)-(3x+6))=0 \)
\( 2(x(x+2)-3(x+2)) =0\)
\(2((x-3)(x+2)) =0 \)
\( (x-3)=0 ,and, (x+2)=0 \)
x=3 and x=-2

Answer 16

So your x equals 3 and -2 NOT -3 and 2

Answer 17

I hope u come back on and see this, I was just busy with smth else and didnt have time to respond