Question

Solve 8(2 1/2x-3/4) - 1/4(1-x)=1/2??

Could somebody please explain these workings

8(5x/2 -3/4) - (1-x)/4=1/2
8((10x-3)/4) -(1-x)/4 = 2/4 (how is it now 2/4???)
(what happened to 5x/2)
80x-24-1+x=2
81x=27
x=27/81

x=1/3

Answer 1

it is hard to read. it the original equation
\[8(2\tfrac{1}{2}x-\frac{3}{4})-\frac{1}{4}(1-x)=\frac{1}{2}\]?

Answer 2

yes

Answer 3

and this is a worked out solution given to you?

Answer 4

yes

Answer 5

ok we can follow it as silly as it is

Answer 6

step one
\[2\tfrac{1}{2}=\frac{5}{2}\] right?

Answer 7

right

Answer 8

so we get
\[8(\frac{5}{2}x-\frac{3}{4})-\frac{1}{4}(1-x)=\frac{1}{2}\]

Answer 9

right

Answer 10

step two is to rewrite
\[\frac{5}{2}x-\frac{3}{4}=\frac{10x-3}{4}\]apparently. that is just adding up the fractions using a common denominator of 4

Answer 11

i think maybe that is where you got confused

Answer 12

where is the 8?

Answer 13

oh i got it

Answer 14

ok it is still there, i was just showing one step

Answer 15

if that is clear, that is where the
\[\frac{5}{2}\]went

Answer 16

now we have
\[8(\frac{10x-3}{4})-\frac{1}{4}(1-x)=\frac{1}{2}\]

Answer 17

as for why is
\[\frac{1}{2}=\frac{2}{4}\] it is because they are clearly the same number. multiply top and bottom by 2 and you get it

Answer 18

and the reason they wrote
\[\frac{2}{4}\] instead of
\[\frac{1}{2}\] is because now the denominator on the left is the same as the one on the right, so you can just get rid of it.

Answer 19

that is why the next line should be
\[8(10x-3)-(1-x)=2\]

Answer 20

oh ok

Answer 21

don't get attached to this way of solving the problem. you can do it any way that you like. you can pick your own order to distribute, combine like terms etc. this is not the way i would have solved this

Answer 22

what way would you of solved this???

Answer 23

after i got rid of the stupid mixed number and saw
\[8(\frac{5}{2}x-\frac{3}{4})-\frac{1}{4}(1-x)=\frac{1}{2}\] i probably would have distributed and get
\[20x-24-\frac{1}{4}(1-x)=\frac{1}{2}\]

Answer 24

then * by 4

Answer 25

then maybe multiply both sides by 4 to clear the fraction. but any way will work

Answer 26

exactly!

Answer 27

gotta run. good luck

Answer 28

thank you