Question

How do you solve `5/8+3/4x=1/16`?

Answer 1

`x=-3/4`

Explanation:

Notice that all the denominators are factors of 16

`(5/8xx2/2)+(3/4xx4/4)x=1/6`

'~~~~~~~~~~~~~~~~ Explaining an idea ~~~~~~~~~~~~~~~~~~~~~~~~
`color(brown)("Note that "2/2" and "4/4" are equivalent to the value of 1")`

#color(brown)("So, in effect "5/8xx2/2" is equivalent to "5/8xx1" and ")#
`color(brown)(3/4xx4/4" is equivalent to "3/4xx1)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`10/16+12/16x=1/16`

Multiply everything by 16

`10+12x=1`

Subtract 10 from both sides

`12x=1-10`

Divide both sides by 12

`x=-9/12 = -3/4`