Question

How do you solve `\frac { q + 2} { 5} + \frac { q - 4} { 4} = \frac { 6} { 5}`?

Answer 1

`color(green)(q=4)`

Explanation:

We can clear the denominators by multiplying all terms on both sides by the LCM (Least Common Multiple) of the given denominators. In this case the LCM of `4 and 5` is `20`.

So
`color(white)("XXX")(q+2)/5 color(blue)( * 20)+(q-4)/4 color(blue)( * 20) = 6/5color(blue)( * 20)`

`color(white)("XXX")(q+2) * color(blue)4 +(q-4) * color(blue)5 = 6 * color(blue)4`

`color(white)("XXX")(4q+8) + (5q-20)=24`

`color(white)("XXX")9q-12 =24`

`color(white)("XXX")9q=36`

`color(white)("XXX")q=4`