Question

How do you solve and check `\frac { x + 2} { 16} = \frac { 1} { 8} + \frac { x - 3} { 3}`?

Answer 1

`x=48/13`

Explanation:

Make all the denominators the same. I deliberately choose 16 to demonstrate a point with the denominator of 3.

`color(green)((x+2)/16=[1/8color(red)(xx1)]+[(x-3)/3color(red)(xx1)]`

`color(green)((x+2)/16=[1/8color(red)(xx2/2)]+[(x-3)/3color(red)(xx(16/3)/(color(white)(.)16/3color(white)(.)))]`

`(x+2)/16=2/16+(16/3(x-3))/16`

Multiply all of both sides by 16 and we have:

`x+cancel(2)=cancel(2)+16/3(x-3)`

Multiply both sides by 3

`3x=16x-48`

`13x=48`

`x=48/13`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check:

`(x+2)/16=1/8+(x-3)/3" "->" "(48/13+2)/16 = 1/8+(48/13-3)/3`

`" "->" "37/104=37/104`

LHS = RHS `=>" True"`